Answer to Question #137055 in Discrete Mathematics for Kyle

Question

7-13: Find the Truth Value (show your solution)
7. Suppose p is false, q is false, s is true. Find the truth value of (s ∨ p) ∧ (q∧ ┐s)
8. Suppose p is true, q is true, r is false, s is false. Find the truth value of (s ∨ p) ∧ (┐r ∨ ┐s)
9. Suppose p is true, q is true, s is false. Find the truth value of (┐s ∨ p) ∨ (q ∧ ┐s)
10. Suppose p is false, s is false, r is true. Find the truth value of ┐ [(s ∧ p) ∨ ┐r]
11. Suppose p is false, q is true, s is true. Find the truth value of (p ∧ ┐q) ∨ ┐s
12. Suppose p is false, q is true, r is false. Find the truth value of (p ∨ ┐q) ∨ r
13. Suppose p is true, q is true, r is true, s is false. Find the truth value of (┐p ∨ s) ∨ (s ∧ r)
14-15: Make a truth table for the given expression.
14. (┐p ∧ q) ∨ (p ∧ ┐q)
15. (┐p ∧ q) (┐p ∨ q)

Answer 1

7.) p=0 q=0 s=1         

(s ∨ p) ∧ (q ∧ ┐s)=0

1.)   (s ∨ p)= (1 ∨ 0)=1

2.)   (q ∧ ┐s)= (0 ∧ ┐1)=0

3.)   (s ∨ p) ∧ (q ∧ ┐s)= 1 ∧ 0 =0

8.)p=1 q=1 r=0 s=0

(s ∨ p) ∧ (┐r ∨ ┐s)=1

1.)   (s ∨ p) = (0 ∨ 1)=1

2.)   (┐r ∨ ┐s)= (┐0 ∨ ┐0)=1

3.)   (s ∨ p) ∧ (┐r ∨ ┐s)=1 ∧ 1 =1

9.)p=1 q=1 s=0

(┐s ∨ p) ∨ (q ∧ ┐s)=1

1.)   (┐s ∨ p)= (┐0 ∨ 1)=1

2.)   (q ∧ ┐s)= (1 ∧ ┐0)

3.)   (┐s ∨ p) ∨ (q ∧ ┐s)= 1 ∨ 1=1

 

10.)p=0 s=0 r=1

┐ [(s ∧ p) ∨ ┐r]= ┐(s ∧ p) ∧  r=1

1.)   (s ∧ p)= (0 ∧ 0)=0

2.)   ┐ (s ∧ p) ∧ r=┐0 ∧ 1=1

 

11.)p=0 q=1 s=1

(p ∧ ┐q) ∨ ┐s=0

1.)   (p ∧ ┐q)= (0 ∧ ┐1)=0

2.)   (p ∧ ┐q) ∨ ┐s=0 ∨ ┐1=0

12.)p=0 q=1 r=0

(p ∨ ┐q) ∨ r=0

1.)   (p ∨ ┐q)= (0 ∨ ┐1)=0

2.)   (p ∨ ┐q) ∨ r=0 ∨ 0=0

 

13.)p=1 q=1 r=1 s=0

(┐p ∨ s) ∨ (s ∧ r)=1

1.)   (┐p ∨ s) =(┐1 ∨ 0)=0

2.)   (s ∧ r)= (0 ∧ 1)=0

3.)   (┐p ∨ s) ∨ (s ∧ r)= 0 ∨ 0=0

 

14.)(┐p ∧ q) ∨ (p ∧ ┐q)=p⊕q

p | q | result

0 | 0 | 0

0 | 1 | 1

1 | 0 | 1

1 | 1 | 0

15.) (┐p ∧ q) (┐p ∨ q)= (┐p ∧ q ∧┐p ) ∨ (┐p ∧ q ∧ q )= ┐p ∧ q

p | q | result

0 | 0 | 0

0 | 1 | 0

1 | 0 | 1

1 | 1 | 0