Engineering
Mathematics
Logical Operator Reasoning Conditional and Bi Conditional
Question
Consider
Statement‑1: (p ⋀ ~ q) ⋀ (~ p ⋀ q) is a fallacy.
Statement‑2: (p → q) ⇔ (~ q ~ p) is a tautology.
Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.
Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA
Solution
Statement‑I: (p ∧ ~ q) ∧ (~ p ∧ q) ~ (p → q) ∧ ~ (q ∧ p)
| p | q | ~ (p → q) S | ~ (q → p) T | S ⋀ T |
| T | F | T | F | F |
| T | T | F | F | F |
| F | F | F | F | F |
| F | T | F | T | F |
Statement‑I is true.
Statement‑II: (p → q) ↔ (~ q → ~ p)
(~ q → ~ p) is equivalent to (p → q)
(p → q) ↔ (p → q)
Hence, (p → q) ↔ (~ q → ~p) is tautology.
Statement-II is true but not correct explanation Statement-I.