Question
Mathematics Question on solution of system of linear inequalities in two variables
The boolean expression (~(p ∧q)) ∨q is equivalent to:
A
q→ (p ∧q)
B
p→q
C
p→ (p→q)
D
p→ (p∨q)
Answer
p→ (p→q)
Explanation
Solution
( (p∧q))∨qis equivalent to :
The following is the truth table
| p | q | p ∧ q | ~p ∧ q | (~(p ∧ q)) ∨ q | p ∨ q | p → q | p → (p ∨ q) |
|---|---|---|---|---|---|---|---|
| T | T | T | F | T | T | T | T |
| T | F | F | T | T | T | F | T |
| F | T | F | T | T | T | T | T |
| F | F | F | T | T | F | T | T |
| Tautology | Tautology |
Hence, (∼(p∧q))∨q≡p→(p∨q)
Hence, the correct option is (D): p→(p∨q)