Choose the correct option.
Statement 1:(p ∧∼ q)∧(∼ p∧q) is a fallacy.
Statement 2:(p⇒q)⇔(∼ q⇒∼ p) is a tautology.
If a logical compound statement always produces the truth (true value), then it is called a tautology.
The opposite of tautology is called fallacy or contradiction, in which the compound statement is always false.
(p ∧∼ q)∧(∼ p∧q)
Using Set Theory approach, this can be expressed as:
Clearly, the resultant is ϕ.
Hence, statement 1 is a fallacy.
(p⇒q)⇔(∼ q⇒∼ p)
Clearly, (∼ q⇒∼ p) is a contra-positive of (p⇒q) and vice-versa.
Hence, statement 2 is a tautology.
Hence, the correct option is C Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1.