Discussion Forum



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


A) Statement I is true, statement II is true; statement II is a correct explanation for statement I

B) Statement I is true, statement II is true; statement II is not a correct explanation for statement I

C) statement I is true ; Statement II is false

D) statement I is false ; Statement II is true

Answer:

Option B

Explanation:

statement II

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

$\equiv (p\rightarrow q)\leftrightarrow (p\rightarrow q)$

 which is always true, so statement II is true.

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

 $\equiv p \wedge \sim q \wedge \sim p \wedge q$

  $\equiv p \wedge \sim p \wedge \sim q \wedge q$

  $\equiv f\wedge f\equiv f$

 Hence, it is a fallacy statement

 So, statement I is true