Maharashtra State BoardHSC Arts 12th Board Exam
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Write the negation of the following. Quadrilateral is a square if and only if it is a rhombus. - Mathematics and Statistics

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Sum

Write the negation of the following.

Quadrilateral is a square if and only if it is a rhombus.

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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.

Concept: Negations of Compound Statements
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