Question

Which one of the following is not equivalent to p $\leftrightarrow$ q ?

• A. $(\rightharpoondown p\vee q)\wedge (p\vee \rightharpoondown q)$
• B. $(\rightharpoondown p\vee q)\wedge (q\to p)$
• C. $(\rightharpoondown p\wedge q)\vee (p\wedge \rightharpoondown q)$
• D. $(\rightharpoondown p\wedge \rightharpoondown q)\vee (p\wedge q)$

Answer 1

The correct option is C $(\rightharpoondown p\wedge q)\vee (p\wedge \rightharpoondown q)$

Here, option (a) and (b) can be reduced to (p$\to q)\wedge (q\to p)$ and hence $\equiv p\leftrightarrow q$
Option(d) is $p^{\prime }{q}^{\prime }$ + $pq$ $\equiv p\leftrightarrow q$
Option (c) is $p{}^{\prime }q$ + $pq{}^{\prime }$ = p $⨁$ p which is not equaivalent to $p\leftrightarrow q$.