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Question
The Boolean expression (~(p ∧ q)) ∨ q is equivalent to ______.
Options
q → (p ∧ q)
p → q
p → (p → q)
p → (p ∨ q)
MCQ
Fill in the Blanks
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Solution
The Boolean expression (~(p ∧ q)) ∨ q is equivalent to p → (p ∨ q).
Explanation:
Given expression is (~(p ∧ q)) ∨ q
= (~ p ∨ ~ q)) ∨ q = ~ p ∨ ~ q ∨ q = ~ p ∨ T
Make the truth table
| p | q | p ∧ q | ~ (p ∧ q) | ~ (p ∧ q) ∨ q | p ∨ q | p → (p ∨ q) |
| T | T | T | F | T | T | T |
| T | F | F | T | T | T | T |
| F | T | F | T | T | T | T |
| F | F | F | T | T | F | T |
p → (p ∨ q) is also a tautology.
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