Question

If $p,q,r$ denote arbitrary statements, then the logically equivalent of the statement $p\Rightarrow (q\vee r)$, is

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

Answer 1

The correct option is B $(p\Rightarrow q)\vee (p\Rightarrow r)$

p q r $q\vee rp\Rightarrow (q\vee r)(p\Rightarrow q)\vee (p\Rightarrow r)$
T T T T T T
T T F T T T
T F T T T T
T F F F F F
F T T T T T .
F T F T T T
F F T T T T
F F F F T T