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JEE Main2013MathematicsMathematical ReasoningActual

Consider : Statement - I : p ∧ ~ q ∧ ~ p ∧ q is a fallacy. Statement - II : p → q ↔ ~ q → ~ p is a tautology.

Options

  1. AStatement - I is true; statement - II is false.
  2. BStatement - I is false; Statement - II is true.
  3. CStatement - I true; Statement - II is true; Statement - II is a correct explanation for Statement - I .
  4. DStatement - I is true; Statement - II is true; Statement - II is not a correct explanation for Statement - I .

Correct answer

D. Statement - I is true; Statement - II is true; Statement - II is not a correct explanation for Statement - I .

Step-by-step solution

The truth table for Statement I is p q ~ p ~ q p ∧ ~ q ~ p ∧ q p ∧ ~ q ∧ ~ p ∧ q T T F F T F T F F F T T F T F T F T F F F F T F F F F F Hence, it is a fallacy. The truth table for statement II is p q ~ p ~ q p → q ~ q → ~ p p → q ↔ ~ q → ~ p T T F F T F T F F F T T F T F T T F T T T F T T T T T T Hence, it is a tautology. But, the second statement is not a correct explanation for the first.

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