First slide

Introduction to mathematical reasoning

Question

The negation of the statement, 'if a quadrilateral is a square, then it is a rhombus' is

Moderate

A

if a quadrilateral is not a square, then it is a rhombus
B

if a quadrilateral is a square, then it is not a rhombus
C

a quadrilateral is a square and it is not a rhombus
D

a quadrilateral is not a square and it is a rhombus

Solution

Let p and q be the propositions as given below
p : A quadrilateral is a square
q: A quadrilateral is a rhombus
The given proposition is $p \to q$
now, $~ (p \to q) ≅ p \land ~ q$
Therefore, the negation of the given proposition is 'A quadrilateral is a square and it is not a rhombus"

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