Truth Tables

GeometryUnit 11, Lesson 6

Mrs. King

Definition

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

Negation Truth Table

p ~p

T

F

Truth Values

Conjunctions are true ONLY when BOTH statements are true.

Look at the example in your notes packet.

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!

Truth Values

Disjunctions are true if AT LEAST ONE statement is true.

Look at the example in your notes packet.

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!

Constructing Truth Tables

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

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

p^~q

p q ~q p^~q

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.

p^~q

p q ~q p^~q

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.

p^~q

p q ~q p^~q

T T

T F

F T

F F

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.

p^~q

p q ~q p^~q

T T F

T F T

F T F

F F T

Make a truth table for ~pvq

p q ~p ~pvq

T T

T F

F T

F F

Make a truth table for ~pv~q

p q ~p ~q ~pv~q

T T

T F

F T

F F

Truth table for (pvq) ^ ~q

p q ~q pvq (pvq)^~q

T T

T F

F T

F F