Mathematical Logic And Boolean Algebra Question 101

Question: The statement $ p\to (p\to q) $ is equivalent to

Options:

A) $ p\to (p\to q) $

B) $ p\to (p,\vee q) $

C) $ p\to (p,\wedge q) $

D) $ p\to (prightarrow q) $

Show Answer

Answer:

Correct Answer: B

Solution:

[b] $ p\to (q\to p)=-p(q\to p) $ $ =\sim p\vee (\sim q\vee p) $ (Since $ p\vee \sim p $ is always true) $ =\sim p\vee p\vee q=p\to (p\vee q) $