UNIT 01 – LESSON 10 - LOGIC ESSENTIAL QUESTION HOW DO YOU USE LOGICAL REASONING TO PROVE STATEMENTS ARE TRUE? SCHOLARS WILL DETERMINE TRUTH VALUES OF NEGATIONS,

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Presentation transcript:

UNIT 01 – LESSON 10 - LOGIC ESSENTIAL QUESTION HOW DO YOU USE LOGICAL REASONING TO PROVE STATEMENTS ARE TRUE? SCHOLARS WILL DETERMINE TRUTH VALUES OF NEGATIONS, CONJUNCTIONS, AND DISJUNCTIONS REPRESENT CONJUNCTIONS AND DISJUNCTIONS USING VENN DIAGRAMS

HOW DO YOU DETERMINE TRUTH VALUE?

HOW DO YOU FIND THE TRUTH VALUE OF A CONJUNCTION?

USE THE FOLLOWING STATEMENTS TO WRITE A COMPOUND STATEMENT FOR THE CONJUNCTION ~P  R. THEN FIND ITS TRUTH VALUE. P: ONE FOOT IS 14 INCHES. Q: SEPTEMBER HAS 30 DAYS. R: A PLANE IS DEFINED BY THREE NONCOLLINEAR POINTS.

HOW DO YOU FIND THE TRUTH VALUE OF A DISJUNCTION?

WHAT DOES A TRUTH TABLE FOR CONJUNCTIONS AND DISJUNCTIONS LOOK LIKE? CONJUNCTION (AND) pQ TTT TFF FTF FFF DISJUNCTION (OR) pq TTT TFT FTT FFF

HOW DO YOU CONSTRUCT TRUTH TABLES USING CONJUNCTIONS, DISJUNCTIONS, AND NEGATIONS? CONSTRUCT A TRUTH TABLE FOR ~P  Q. CONSTRUCT A TRUTH TABLE FOR P  (~Q  R). CONSTRUCT A TRUTH TABLE FOR (P  Q)  (Q  R)

HOW DO YOU USE A VENN DIAGRAM TO ILLUSTRATE CONJUNCTIONS & DISJUNCTIONS? IN A VENN DIAGRAM… THE CONJUNCTION IS REPRESENTED BY THE INTERSECTION OF TWO SETS. THE INTERSECTION OF TWO SETS IS THE SET OF ELEMENTS THAT ARE COMMON TO BOTH. THE DISJUNCTION IS REPRESENTED BY THE UNION OF TWO SETS. THE UNION OF TWO SETS IS THE SET OF ELEMENTS THAT APPEAR IN EITHER OF THE SETS.

HOW DO YOU INTERPRET A VENN DIAGRAM? DANCING THE VENN DIAGRAM SHOWS THE NUMBER OF STUDENTS ENROLLED IN MONIQUE’S DANCE SCHOOL FOR TAP, JAZZ, AND BALLET CLASSES. A. HOW MANY STUDENTS ARE ENROLLED IN ALL THREE CLASSES? THE STUDENTS THAT ARE ENROLLED IN ALL THREE CLASSES ARE REPRESENTED BY THE INTERSECTION OF ALL THREE SETS. THERE ARE 9 STUDENTS ENROLLED IN ALL THREE CLASSES. B. HOW MANY STUDENTS ARE ENROLLED IN TAP OR BALLET? THE STUDENTS THAT ARE ENROLLED IN TAP OR BALLET ARE REPRESENTED BY THE UNION OF THESE TWO SETS. THERE ARE OR 121 STUDENTS ENROLLED IN TAP OR BALLET. C, HOW MANY STUDENTS ARE ENROLLED IN JAZZ AND BALLET, BUT NOT TAP? THE STUDENTS THAT ARE ENROLLED IN JAZZ AND BALLET, BUT NOT TAP, ARE REPRESENTED BY THE INTERSECTION OF JAZZ AND BALLET MINUS ANY STUDENTS ENROLLED IN TAP. THERE ARE – 9 OR 25 STUDENTS ENROLLED IN JAZZ AND BALLET, BUT NOT TAP.