Question

~(p<->q) equivalent to ~(p)<->q
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Answer 1

Answer:

In logic and mathematics, statements {\displaystyle p}p and {\displaystyle q}q are said to be logically equivalent if they are provable from each other under a set of axioms,[1] or have the same truth value in every model.[2] The logical equivalence of {\displaystyle p}p and {\displaystyle q}q is sometimes expressed as {\displaystyle p\equiv q}p \equiv q, {\displaystyle p::q}{\displaystyle p::q},[3] {\displaystyle {\textsf {E}}pq}{\displaystyle {\textsf {E}}pq}, or {\displaystyle p\iff q}{\displaystyle p\iff q}, depending on the notation being used. However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concepts are intrinsically related.

Answer 2

Step-by-step explanation:

Contrapositive: The contrapositive of a conditional statement of the form "If p then q" is "If ~q then ~p". Symbolically, the contrapositive of p q is ~q ~p. A conditional statement is logically equivalent to its contrapositive.

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