JEE Main 2013 (Offline)Question 1
Consider : Statement - I : $(p\wedge\sim q)\wedge(\sim p\wedge q)$ is a fallacy. Statement - II : $(p\rightarrow q)\leftrightarrow(\sim q\rightarrow\sim p)$ is a tautology.
Mathematical Reasoning
Solution
$(p\wedge\sim q)\wedge(\sim p\wedge q)$ contains $p\wedge\sim p$, so it is always false (fallacy). $p\to q\equiv\sim q\to\sim p$ (contrapositive), so II is a tautology. Both true, but II does not explain I.