Question

The logically equivalent proposition of $p\iff q$ is

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

Answer 1

Answer: (B)

Lets form the truth table,

$\begin{array}{ccccccc}p& q& p\iff q& (p\wedge q)\vee (p\wedge q)& (p\wedge q)\vee (q\Rightarrow p)& (p\Rightarrow q)\vee (q\Rightarrow p)& (p\wedge q)\Rightarrow (q\vee p)\\ T& T& T& T& T& T& T\\ T& F& F& T& F& F& T\\ F& T& F& T& T& F& T\\ F& F& T& F& T& T& T\end{array}$

From the table, $(p\Rightarrow q)\wedge (q\Rightarrow p)$ means $p\iff q$.

Hence, option is C is correct.