Question

Consider the following statements:
Statement I : $(p\wedge \sim q)\wedge (\sim p\wedge q)$ is a fallacy.
Statement II : $(p\to q)\leftrightarrow (\sim q\to \sim p)$ is a tautology.

• A. Statement I is True; Statement II is true; Statement II is not a correct explanation for Statement I
• B. Statement I is True; Statement II is False
• C. Statement I is False; Statement II is True
• D. Statement I is True; Statement II is True; Statement II is a correct explanation for Statement I

Answer 1

The correct option is A Statement I is True; Statement II is true; Statement II is not a correct explanation for Statement I

STATEMENT 1

Truth table for (p$\wedge$ $\sim$q)$\wedge$ ($\sim$p$\wedge$ q).

p q $\sim$p $\sim$q (p$\wedge$ $\sim$q) ($\sim$p$\wedge$ q) (p$\wedge$ $\sim$q)$\wedge$ ($\sim$p$\wedge$ q)

T T F F F F F

T F F T T F F

F T T F F T F

F F T T F F F

Therefore, (p$\wedge$ $\sim$ q)^($\sim$ p$\wedge$ q) is a FALLACY.

Statement 1 is TRUE.

STATEMENT 2

Truth table for (p$\to$q)$\leftrightarrow$ ($\sim$q$\to$$\sim$p).

p q $\sim$p $\sim$q p$\to$q $\sim$q$\to$$\sim$p (p$\to$q)$\leftrightarrow$ ($\sim$q$\to$$\sim$p)

T T F F T T T

T F F T F F T

F T T F T T T

F F T T T T T

Therefore, statement 2 is a TAUTOLOGY.

Statement 2 is TRUE.

Also, Statement 2 is not correct explanation of Statement 1.

Therefore, option (A) is the correct answer.