Question

the negation of the bi-conditional : p⇔q, where p,q are logical propositions, is a) p⊕q (where ⊕ is the exclusive-or logical operator) b) (¬p⟹¬q)∧(¬q⟹¬) c) (¬p⇒q)∨(¬q⟹p)

Answer 1

The negation of the bi-conditional p⇔q is option c) (¬p⇒q)∨(¬q⟹p).

Step-by-step explanation:

The negation of the bi-conditional p⇔q is option c) (¬p⇒q)∨(¬q⟹p).

To understand why, let's break down the negation of a bi-conditional. The bi-conditional p⇔q is true when both p and q have the same truth value (either both true or both false). Therefore, the negation of the bi-conditional is true when p and q have different truth values. In other words, one of them is true and the other is false.

Option c) (¬p⇒q)∨(¬q⟹p) expresses this condition. If p is true and q is false, then ¬p⇒q is true. If p is false and q is true, then ¬q⟹p is true. Therefore, the whole expression is true when the truth values of p and q are different, which is the negation of the bi-conditional.