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Question
Let Δ ∈ {∧, ∨, ⇒, ⇔}be such that (p ∧ q)Δ((p ∨ q) ⇒ q) is a tautology. Then Δ is equal to ______.
Options
∧
∨
⇒
⇔
MCQ
Fill in the Blanks
Solution
Let Δ ∈ {∧, ∨, ⇒, ⇔}be such that (p ∧ q)Δ((p ∨ q) ⇒ q) is a tautology. Then Δ is equal to ⇒.
Explanation:
| p | q | p ∨ q | (p ∨ q) ⇒ q | p ∧ q | (p ∧ q)∧ (p ∨ q) ⇒ q) |
(p ∧ q)∨ ((p ∨ q) ⇒ q) |
(p ∧ q) ⇒ ((p ∨ q) ⇒ q) |
(p ∧ q) ⇔ (( p ∨ q) ⇒ q) |
| T | T | T | T | T | T | T | T | T |
| T | F | T | F | F | F | F | T | T |
| F | T | T | T | F | T | T | T | F |
| F | F | F | T | F | F | T | T | F |
Clearly, (p ∧ q) ⇒ ((p ∨ q) ⇒ q) is a tautology.
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Tautology, Contradiction, and Contingency
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