Question

Consider the following statements:

Statement I:$(p\wedge ~q)\wedge (~p\wedge q)$ is a fallacy.

Statement II: $(p\to q)\leftrightarrow (~q\to ~p)$ is a tautology.

• A. Statement I is correct, Statement II is correct; Statement II is a correct explanation for Statement I
• B. Statement I is correct; Statement II is correct; Statement II is not a correct explanation for Statement I
• C. Statement I is correct, Statement II is incorrect
• D. Statement I is incorrect, and Statement II is correct

Answer 1

The correct option is B

Statement I is correct; Statement II is correct; Statement II is not a correct explanation for Statement I

Explanation for the correct option:

Step 1. Check Statement II :

Statement II: $(p\to q)\leftrightarrow (~q\to ~p)\equiv (p\to q)\leftrightarrow (p\to q)$ which is always true.

So, statement II is true.

Step2. Check Statement I :

Statement I:$\begin{array}{rcl}& & (p\wedge ~q)\wedge (~p\wedge q)\end{array}$

$\begin{array}{rcl}& =& (p\wedge ~q)\wedge (~p\wedge q)\\ & =& (p\wedge ~p)\wedge (~q\wedge q)\\ & =& F\wedge F\\ & =& F\end{array}$

So, it is a fallacy statement.

Thus, Statement I is correct; Statement II is correct; Statement II is not a correct explanation for Statement I

Hence, the correct option is B.