Page 175 - Math Course 2 (Book 2)

Truth Tables and Logic

Construct Truth Tables
Construct a truth table for p v (~q ⋀ r).
Example Step 1

Make columns with the headings p, q, r, ~q, ~q ⋀ r,
and p ⋁ (~q ⋀ r).
Construct a truth table for ~p ⋁ q.

Step 1 p q r ~q ~q ⋀ r p ⋁ (~q ⋀ r)
Make columns with the heading p, q, ~p, and ~p v q.

p q ~p ~p ⋁ q

Step 2
List the possible combinations of truth values for p
and q. Step 2

p q ~p ~p ⋁ q List the possible combinations of truth values for p,
q, and r.
T T p q r ~q ~q ⋀ r p ⋁ (~q ⋀ r)
T F T T T
T F T
F T
T T F
F F T F F

Step 3 F T T
Use the truth values of p to determine the truth F F T
values of ~p.
F T F
p q ~p ~p ⋁ q F F F

T T F
T F F Step 3
Use the truth values of q to determine the truth
F T T
values of ~q.
F F T
p q r ~q ~q ⋀ r p ⋁ (~q ⋀ r)
Step 4 T T T F
Use the truth values of ~p and q to write the truth
values for ~p v q. T F T T
Answer T T F F
p q ~p ~p ⋁ q T F F T
F T T F
T T F T
F F T T
T F F F
F T F F
F T T T
F F F T
F F T T

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