Question

The statement $(\rightharpoondown p)\Rightarrow (\rightharpoondown q)$ is logically equivalent to which of the statements below?

I $p\Rightarrow q$
II $q\Rightarrow p$
III $(\rightharpoondown q)\vee p$
IV $(\rightharpoondown p)\vee q$

• A. I only
• B. I and IV only
• C. II only
• D. II and III only

Answer 1

The correct option is D II and III only

Statement $p{}^{\prime }\Rightarrow q{}^{\prime }\equiv p+q{}^{\prime }$
I. $p\to q\equiv p{}^{\prime }+q$
II. $q\to p\equiv q{}^{\prime }+p$
III. $(\rightharpoondown q\vee p)\equiv q{}^{\prime }+p$
IV. $(\rightharpoondown p\vee q)\equiv p{}^{\prime }+q$
So , clearly the given statement is same as II and III only.