1Everyone that Michael likes likes either Henry or Sue 2Michael likes everyone that both Sue and Rita like 3Michael likes everyone that either Sue or Rita.

Slides:

Advertisements

Similar presentations

Indefinite Pronouns.

Advertisements

This is a self running presentation that lasts about 4 minutes, and loops continuously until escape is pressed. The text appears one word at a time to.

1Everyone that Michael likes likes either Henry or Sue 2Michael likes everyone that both Sue and Rita like 3Michael likes everyone that either Sue or Rita.

Most-to-Least Legible Color Combinations for Viewing on Slide Shows Color and contrast are very important tools in communication. They can be used to enhance.

Exam #3 will be given on Monday Nongraded Homework: Now that we are familiar with the universal quantifier, try

PRONOUNS LESSON 1. WHAT IS A PRONOUN? Pronouns take the place of nouns to name persons, places, things, or ideas.

Predicate Logic and the language PL  In SL, the smallest unit is the simple declarative sentence.  But many arguments (and other relationships between.

Test 4 Review For test 4, you need to know: Definitions the recursive definition of ‘formula of PL’ atomic formula of PL sentence of PL bound variable.

FOL Practice. Models A model for FOL requires 3 things: A set of things in the world called the UD A list of constants A list of predicates, relations,

1 Press Ctrl-A ©G Dear 2008 – Not to be sold/Free to use Binomial Products Stage 6 - Year 11 Mathematic (Preliminary)

Proofs in Predicate Logic A rule of inference applies only if the main operator of the line is the right main operator. So if the line is a simple statement,

(using first-order predicate logic)

For Wednesday, read chapter 6, section 1. As nongraded HW, do the problems on p Graded Homework #7 is due on Friday at the beginning of class. In.

For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the.

Review Test 5 You need to know: How to symbolize sentences that include quantifiers of overlapping scope Definitions: Quantificational truth, falsity and.

1. 2 EXAM #3 25 translations from English into Predicate Logic 4 points each Only final formula is graded. Do intermediate work on scratch paper.

Predicate Logic (PL) 1.Syntax: The language of PL Formula VS. Sentence Symbolize A-, E, I-, and O-sentences 2.Semantic: a sentence compare two sentences.

March 5: more on quantifiers We have encountered formulas and sentences that include multiple quantifiers: Take, for example: UD: People in Michael’s office.

Formal Logic Mathematical Structures for Computer Science Chapter 1 Copyright © 2006 W.H. Freeman & Co.MSCS SlidesFormal Logic.

PL continued: Quantifiers and the syntax of PL 1. Quantifiers of PL 1. Quantifier symbols 2. Variables used with quantifiers 2. Truth functional compounds.

Symbolization in Predicate Logic In Predicate Logic, statements predicate properties of specific individuals or members of a group. Singular Statement:

No man will lift a lance against another. There never was much undergrowth in Boeotia, Such a smooth place, and this girl takes after it. All woes shall.

Two-digit Addition 2.NBT.6. Joseph likes collecting stamps. He has 24 stamps from different Asian countries, 32 stamps showing different parks in the.

Predicate Logic What is a predicate? A property that can be attributed to --or said of –a thing. Being greenBeing contingent Being four feet tall Being.

Notes Over 12.5 Probability of Independent Events 1. You are playing a game with 2 numbered cubes. Find the probability of rolling a sum of 8 on the first.

Formal Logic Mathematical Structures for Computer Science Chapter Copyright © 2006 W.H. Freeman & Co.MSCS SlidesFormal Logic.

Proofs in Predicate Logic A rule of inference applies only if the main operator of the line is the right main operator. So if the line is a simple statement,

What are some words that come to mind when you hear the word ALGEBRA? From the grade 5 class: Math Numbers Operations Algae Measuring.

Difference of Squares Chapter 8.8. Difference of Squares (Definition)

WHITE YELLOW GREEN BLUE RED PINK BLACK BROWN ORANGE.

The bare facts about bears Text types: Information report, quiz.

PART TWO PREDICATE LOGIC. Chapter Seven Predicate Logic Symbolization.

$100 $200 $300 $400 $100 $200 $300 $400 $300 $200 $100 Fraction with pictures Convert mixed to improper fractions Convert improper to mixed fractions.

I Can See. I can see the blue blanket. I can see the brown monkey.

1Everyone that Michael likes likes either Henry or Sue 2Michael likes everyone that both Sue and Rita like 3Michael likes everyone that either Sue or Rita.

Lecture 8 Predicate Logic TF4233 Mathematical Logic Semester 2, 2006/2007 Dr. Rolly Intan & Cherry Ballangan, MAIT Informatics Department, Petra Christian.

GCF vs. LCM What’s the difference?.

80-210: Logic & Proofs July 30, 2009 Karin Howe

Sight Words Shoesmith Kindergarten Mrs. Cranley and Mrs. Stuttley.

I see colors.. I see a blue bird. I see a yellow sun.

SL: Basic syntax - formulae Atomic formulae – have no connectives If P is a formula, so is ~P If P and Q are formulae, so are (P&Q), (P  Q), (P  Q),

Fractions and Sets 9-3 I can show and understand that fractions are equal parts of a whole. 3.NF.1.

An urn contains 1 green, 2 red, and 3 blue marbles. Draw two without replacement. 1/6 2/6 3/6 2/5 3/5 1/5 3/5 1/5 2/5 2/30 3/30 2/30 6/30 3/30 6/30.

Q. A quadratic equation is An equation with 1 solution An equation with 2 solutions An equation with 0 solutions An equation with 3 solutions.

Timed test.  You will see a series of 10 questions.  You have to write down the answer to the question.  Easy enough eh?  REMEMBER TO GIVE PROBABILITIES.

Last Answer LETTER I h(x) = 3x 4 – 8x Last Answer LETTER R Without graphing, solve this polynomial: y = x 3 – 12x x.

Lecture 1-3: Quantifiers and Predicates. Variables –A variable is a symbol that stands for an individual in a collection or set. –Example, a variable.

What colour is it / are they?

GIANT TWISTER!.

A Brief Review of Factoring

Jeopardy Perfect Cubes Factor then Solve Trinomials Binomials Misc.

Red Rockets and Rainbow Jelly (by Sue Heap & Nick Sharratt)

Date of download: 11/16/2017 Copyright © ASME. All rights reserved.

Election #1 Popular Vote Electoral Vote State Red Yellow

Indefinite Pronouns 11 Indefinite pronouns are pronouns that do not refer to a specific noun. Ex. Does anybody know where the post office is? Ex. No one.

Using fractions and percentages

2 Identities and Factorization

Mathematical Structures for Computer Science Chapter 1

What Color is it?.

Which One Doesn’t Belong?

Xuan Guo Lab 3 Xuan Guo

Proofs in Predicate Logic

Predicate Logic Hurley 8.1 Translation.

Point-slope Form of Equations of Straight Lines

WE CAN READ Donald Joyce.

Presentation transcript:

1Everyone that Michael likes likes either Henry or Sue 2Michael likes everyone that both Sue and Rita like 3Michael likes everyone that either Sue or Rita like 4Rita doesn’t like Michael but she likes everyone that Michael likes 5Grizzly bears are dangerous but black bears are not 6Grizzly bears and polar bears are dangerous but black bears are not 7Every self-respecting polar bear is a good swimmer

1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like 3Michael likes everyone that either Sue or Rita like 4Rita doesn’t like Michael but she likes everyone that Michael likes 5Grizzly bears are dangerous but black bears are not 6Grizzly bears and polar bears are dangerous but black bears are not 7Every self-respecting polar bear is a good swimmer

1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like  x(Lsx&Lrx  Lmx) 3Michael likes everyone that either Sue or Rita like 4Rita doesn’t like Michael but she likes everyone that Michael likes 5Grizzly bears are dangerous but black bears are not 6Grizzly bears and polar bears are dangerous but black bears are not 7Every self-respecting polar bear is a good swimmer

1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like  x(Lsx&Lrx  Lmx) 3Michael likes everyone that either Sue or Rita like  x(Lsx  Lrx  Lmx) 4Rita doesn’t like Michael but she likes everyone that Michael likes 5Grizzly bears are dangerous but black bears are not 6Grizzly bears and polar bears are dangerous but black bears are not 7Every self-respecting polar bear is a good swimmer

1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like  x(Lsx&Lrx  Lmx) 3Michael likes everyone that either Sue or Rita like  x(Lsx  Lrx  Lmx) 4Rita doesn’t like Michael but she likes everyone that Michael likes ~Lrm &  x(Lmx  Lrx) 5Grizzly bears are dangerous but black bears are not 6Grizzly bears and polar bears are dangerous but black bears are not 7Every self-respecting polar bear is a good swimmer

1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like  x(Lsx&Lrx  Lmx) 3Michael likes everyone that either Sue or Rita like  x(Lsx  Lrx  Lmx) 4Rita doesn’t like Michael but she likes everyone that Michael likes ~Lrm &  x(Lmx  Lrx) 5Grizzly bears are dangerous but black bears are not  x(Gx  Dx) &  x(Bx  ~Dx) 6Grizzly bears and polar bears are dangerous but black bears are not 7Every self-respecting polar bear is a good swimmer

1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like  x(Lsx&Lrx  Lmx) 3Michael likes everyone that either Sue or Rita like  x(Lsx  Lrx  Lmx) 4Rita doesn’t like Michael but she likes everyone that Michael likes ~Lrm &  x(Lmx  Lrx) 5Grizzly bears are dangerous but black bears are not  x(Gx  Dx) &  x(Bx  ~Dx) 6Grizzly bears and polar bears are dangerous but black bears are not  x(Gx  Px  Dx) &  x(Bx  ~Dx) 7Every self-respecting polar bear is a good swimmer

1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like  x(Lsx&Lrx  Lmx) 3Michael likes everyone that either Sue or Rita like  x(Lsx  Lrx  Lmx) 4Rita doesn’t like Michael but she likes everyone that Michael likes ~Lrm &  x(Lmx  Lrx) 5Grizzly bears are dangerous but black bears are not  x(Gx  Dx) &  x(Bx  ~Dx) 6Grizzly bears and polar bears are dangerous but black bears are not  x(Gx  Px  Dx) &  x(Bx  ~Dx) 7Every self-respecting polar bear is a good swimmer  x(Px & Rxx  Sx)

UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita 11If anyone likes Sue, Michael does 12If everyone likes Sue, Michael does 13If anyone likes Sue, he or she likes Rita 14Michael doesn’t like everyone 15Michael doesn’t like anyone 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does 12If everyone likes Sue, Michael does 13If anyone likes Sue, he or she likes Rita 14Michael doesn’t like everyone 15Michael doesn’t like anyone 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does 13If anyone likes Sue, he or she likes Rita 14Michael doesn’t like everyone 15Michael doesn’t like anyone 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does  xLxs  Lms 13If anyone likes Sue, he or she likes Rita 14Michael doesn’t like everyone 15Michael doesn’t like anyone 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does  xLxs  Lms 13If anyone likes Sue, he or she likes Rita  x(Lxs  Lxr) 14Michael doesn’t like everyone 15Michael doesn’t like anyone 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does  xLxs  Lms 13If anyone likes Sue, he or she likes Rita  x(Lxs  Lxr) 14Michael doesn’t like everyone~  xLmx 15Michael doesn’t like anyone 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does  xLxs  Lms 13If anyone likes Sue, he or she likes Rita  x(Lxs  Lxr) 14Michael doesn’t like everyone~  xLmx 15Michael doesn’t like anyone~  xLmx 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does  xLxs  Lms 13If anyone likes Sue, he or she likes Rita  x(Lxs  Lxr) 14Michael doesn’t like everyone~  xLmx 15Michael doesn’t like anyone~  xLmx 16If someone likes Sue, then s/he likes Rita  x(Lxs  Lxr) 17If someone likes Sue, then someone likes Rita

UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does  xLxs  Lms 13If anyone likes Sue, he or she likes Rita  x(Lxs  Lxr) 14Michael doesn’t like everyone~  xLmx 15Michael doesn’t like anyone~  xLmx 16If someone likes Sue, then s/he likes Rita  x(Lxs  Lxr) 17If someone likes Sue, then someone likes Rita  xLxs   xLxr

For 18-28: UD: Ashley, Rhoda, Terry, Clarence and their marbles a, r, t, c stand for Ashley, Rhoda, Terry, Clarence respectively Bxx is blue Gxx is green Rxx is red Sxx is a shooter Cxx is a cat’s-eye Txx is a steely Mx x is a marble Bxyx belongs to y Wxyx wins y Gxyzx gives y to z 18All the cat’s-eyes belong to Rhoda 19All the marbles but the shooters are cat’s-eyes 20Some but not all of the cat’s-eyes are green 21None of the steelies is red green or blue

For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket 43The only pear in the basket is rotten 44There are at least two apples in the basket 45There are two (and only two) apples in the basket 46There are no more than two pears in the basket 47there are at least three apples in the basket

For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten 44There are at least two apples in the basket 45There are two (and only two) apples in the basket 46There are no more than two pears in the basket 47there are at least three apples in the basket

For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx 44There are at least two apples in the basket 45There are two (and only two) apples in the basket 46There are no more than two pears in the basket 47there are at least three apples in the basket

For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx &  y(Py & Nyb  y=x) ) 44There are at least two apples in the basket 45There are two (and only two) apples in the basket 46There are no more than two pears in the basket 47there are at least three apples in the basket

For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx &  y(Py & Nyb  y=x) ) 44There are at least two apples in the basket  x  y(Ax & Nxb & Ay & Nyb 45There are two (and only two) apples in the basket 46There are no more than two pears in the basket 47there are at least three apples in the basket

For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx &  y(Py & Nyb  y=x) ) 44There are at least two apples in the basket  x  y(Ax & Nxb & Ay & Nyb & x  y ) 45There are two (and only two) apples in the basket 46There are no more than two pears in the basket 47there are at least three apples in the basket

For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx &  y(Py & Nyb  y=x) ) 44There are at least two apples in the basket  x  y(Ax & Nxb & Ay & Nyb & x  y ) 45There are two (and only two) apples in the basket  x  y(Ax & Nxb & Ay & Nyb &  z(Az & Nzb  (z=y  z=x) & x  y ) 46There are no more than two pears in the basket 47there are at least three apples in the basket

For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx &  y(Py & Nyb  y=x) ) 44There are at least two apples in the basket  x  y(Ax & Nxb & Ay & Nyb & x  y ) 45There are two (and only two) apples in the basket  x  y(Ax & Nxb & Ay & Nyb &  z(Az & Nzb  (z=y  z=x) & x  y ) 46There are no more than two pears in the basket  x  y(Ax & Nxb & Ay & Nyb &  z(Az & Nzb  (z=y  z=x) ) 47there are at least three apples in the basket

For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx &  y(Py & Nyb  y=x) ) 44There are at least two apples in the basket  x  y(Ax & Nxb & Ay & Nyb 45There are two (and only two) apples in the basket  x  y(Ax & Nxb & Ay & Nyb &  z(Az & Nzb  (z=y  z=x) ) 46There are no more than two pears in the basket  x  y(Ax & Nxb & Ay & Nyb &  z(Az & Nzb  (z=y  z=x) ) 47there are at least three apples in the basket  x  y  z (Ax & Ay & Az & Nxb & Nyb & Nzb & &  w(Aw & Nwb  w=x  w=y  w=z) )