Answer:
Option A
Explanation:
Key Idea Use p\rightarrow q= \sim p \vee q
and p\leftrightarrow q=( \sim p \vee q)\wedge (p \vee \sim q)
Given, p,q \rightarrow T and r,s \rightarrow F
\therefore a:\sim (p \wedge \sim r)\vee (\sim q \vee s)
\equiv \sim(T \wedge T)\vee(F\vee F)
\equiv \sim(T) \vee(F)
\equiv F \vee F= F
and b: \ (p \vee s)\leftrightarrow ( q \wedge r)
\equiv (\sim (p \vee s)\vee(q\wedge r))\wedge ((p \vee s)\vee\sim (q \wedge r))
\because p\leftrightarrow q \equiv(\sim p \vee q)\wedge(p \vee \sim q)
\equiv(\sim (T \vee F)\vee (T \wedge F))\wedge(( T \vee F)\vee \sim(T \wedge F))
\equiv( F \vee F)\wedge(T \vee T)
\equiv F \wedge T\equiv F