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Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not...

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Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or tomorrow is not Friday.
Transcript
Page 1: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Review Given

p: Today is Thursdayq: Tomorrow is Friday

Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and

tomorrow is Friday 2. Today is Thursday or tomorrow

is not Friday.

Page 2: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Truth Tables

GeometryUnit 9, Day 3Mr. Zampetti

Page 3: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Objective

To construct truth tables and determine the truth value of compound statements.

Page 4: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Definition

Truth Table – a convenient way to organize the truth values of statements.

Page 5: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Negation Truth Table

p ~p

T

F

Page 6: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Truth Values

Conjunctions are true ONLY when BOTH statements are true.

Look at the example in your notes packet.

Page 7: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Conjunction Truth Table

p q p^q

T T

T F

F T

F F

Remember a conjunction is only true when BOTH are true!

Page 8: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Truth Values

Disjunctions are true if AT LEAST ONE statement is true.

Look at the example in your notes packet.

Page 9: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Disjunction Truth Table

p q pvq

T T

T F

F T

F F

Remember a disjunction is true when AT LEAST ONE are true!

Page 10: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Constructing Truth Tables

GIVEN: p^~q Step 1: Make columns with

headings p, q, ~q, and p^~q

Page 11: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

p^~q

p q ~q p^~q

Page 12: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Constructing Truth Tables

p^~q Step 1: Make columns with

headings p, q, ~q, and p^~q Step 2: List possibilities of p and q.

Page 13: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

p^~q

p q ~q p^~q

Page 14: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Constructing Truth Tables

p^~q Step 1: Make columns with

headings p, q, ~q, and p^~q Step 2: List possibilities of p and q. Step 3: Determine ~q by using q.

Page 15: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

p^~q

p q ~q p^~q

T T

T F

F T

F F

Page 16: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Constructing Truth Tables

p^~q Step 1: Make columns with

headings p, q, ~q, and p^~q Step 2: List possibilities of p and q. Step 3: Determine ~q by using q. Step 4: Determine p^~q by using

p and ~q.

Page 17: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

p^~q

p q ~q p^~q

T T F

T F T

F T F

F F T

Page 18: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Make a truth table for ~pvq

p q ~p ~pvq

T T

T F

F T

F F

Page 19: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Make a truth table for ~pv~q

p q ~p ~q ~pv~q

T T

T F

F T

F F

Page 20: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Homework

Work Packet: Truth Tables

Page 21: Review Given p: Today is Thursday q: Tomorrow is Friday Write: 1. ~p^q 2. pv~q 1. Today is not Thursday and tomorrow is Friday 2. Today is Thursday or.

Truth table for (pvq) ^ ~q

p q ~q pvq (pvq)^~q

T T

T F

F T

F F


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