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Question
Write the negation of the following.
Quadrilateral is a square if and only if it is a rhombus.
Solution
Let p: Quadrilateral is a square.
q: It is a rhombus.
Then the symbolic form of the given statement is p↔q.
Since ∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p), the negation of the given statement is:
Quadrilateral is a square but it is not a rhombus or quadrilateral is a rhombus but it is not a square.
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