 LOGIC

Use of deductive reasoning to come to a conclusion given a set of information.

 Foundation of logic is the statement  Examples of statements: o Sony is the largest employer in Japan. o It is snowing. o Professor Ryan teaches math.  A statement is a sentence whose truth can be proven or disproven.

 Can you think of a sentence that is NOT a statement?  Hint: You must be able to assign “True” or “False” to a statement.

 Examples: and, or, if…then  And: o “You must feed the meter and you must park between the lines.” o Both  Or: o “You must feed the meter or you must park between the lines.” o One or the other or both (Inclusive OR)

 If…then: o “If the meter maid sees your expired parking meter, then you will get a ticket.” o Relates two ideas.

 Not: o Negation of the statement You will get a ticket. Is You will not get a ticket. (We do not cover all, none, some)

 Compound Statement: o “You must feed the meter and you must park between the lines.”  Two or more statements, each of which can be assigned a truth value, linked by a connective

 Lower case letters represent statements p: You must feed the meter. q: You must park between the lines.

˄ : AND ˅ : OR ~: NOT Do the first two look familiar?

 Example: o You must feed the meter and you must park between the lines. o Let: p: You must feed the meter q: You must park between the lines. ˄ : AND p ˄ q CONJUCTION

 Example: o You must feed the meter or you must park between the lines. Let: p: You must feed the meter. q: You must park between the lines. ˅ : OR p ˅ q DISJUCTION

 Example: o You must not feed the meter. Let: p: You must feed the meter ~: NOT ~p NEGATION

 Example: o Sony will replace the product AND Sony will NOT credit toward a future purchase. Let: p: Sony will replace the product. q: Sony will give a credit toward a future purchase. ˄ : AND Write the statement in symbolic form:

 Example: o Sony will NOT replace the product and Sony will give a credit toward a future purchase. Let: p: Sony will replace the product. q: Sony will give a credit toward a future purchase ˄ : AND Write the statement in symbolic form:

Let: p: You are 17. q: You may drive legally. Write in words: ~q p ˅ q ~p ˄ q

 Consider: o I know you and I like to go to the movies. o I know you, and I like to go to the movies.

 Used to break up a list into its elements. o He ordered calamari, pasta, dessert and coffee.  Used to separate independent ideas o He ordered dinner, then he called his girlfriend.  Used to clarify compound statements. o Dinner includes soup, salad and the vegetable of the day. o Dinner includes soup, and salad or the vegetable of the day. o Dinner includes soup or salad, and the vegetable of the day.

 Dinner includes soup, salad and the vegetable of the day. o Translation:  Dinner includes soup, and salad or the vegetable of the day. o Translation:  Dinner includes soup or salad, and the vegetable of the day. o Translation:

 Summary: o Simple statement on the same side of a comma are to be grouped together within parentheses.

 Negation of a conjunction: o It is neither warm nor sunny. Let: p: It is warm. q: It is sunny. ~: NOT ^: AND Then ~(p ^ q) Note: ~( ) may be read “It is not the case that…” or “ It is false that…

 If…then symbolized by →  p → q is read “If p, then q”  “If you are over 16, then you may drive.” o p: You are over 16. o q: You may drive. p → q o What does ~p →q mean? o What does ~(p → q) mean?

 Does p v q → r mean (p v q) → r or p v (q → r) ?  Order of Evaluation: o Parentheses first o If no parentheses: ~, ^/v, → o (Conditional last)