Page 176 - Math Course 2 (Book 2)

Truth Tables and Logic

Construct Truth Tables
Step 4
Use the truth values for q and r to write the truth Which sequence of Ts and Fs would correctly
values for ~q ⋀ r. complete the last column of the following truth
table for the given compound statement?
p q r ~q ~q ⋀ r p ⋁ (~q ⋀ r) (p ⋀ q) ⋁ (q ⋀ r)
T T T F F p q r p ⋀ q p ⋀ r (p ⋀ q) ⋁ (p ⋀ r)
T F T T T T T T T T
T T F F F T F T F F

T F F T F T T F T F
F T T F F T F F F F
F F T T T F T T F T
F F T F F
F T F F F
F T F F F
F F F T F
F F F F F

Step 5
Use the truth values for ~q ⋀ r and p to write the A. T B. T C. T D. T
truth values for p ⋁ (~q ⋀ r).
F F F F
Answer
F T F T
p q r ~q ~q ⋀ r p ⋁ (~q ⋀ r)

T T T F F T F F F F
T F T T T T T T F T
T T F F F T F F F F
T F F T F T
T T F F
F T T F F F
F F T T T T F F F F

F T F F F F
F F F T F F Answer

Your Turn!

Use Venn Diagrams

How many students in Manhattan School have one of three types of pets?

A. 226 B. 311
C. 301 D. 110 Answer
dogs cats
How many students have dogs or cats? 47
85 110
A. 57 B. 242 10
C. 252 D. 280 Answer 23 5

How many students have dogs, cats, and birds as pets? birds
31
A. 10 B. 85 Answer
C. 116 D. 311

168