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Show that the Following Statement is True by the Method of Contrapositive. P: If X is an Integer and X2 is Even, Then X is Also Even. - CBSE (Arts) Class 11 - Mathematics

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Question

Show that the following statement is true by the method of contrapositive.

pIf x is an integer and x2 is even, then x is also even.

Solution

p: If x is an integer and x2 is even, then x is also even.

Let qx is an integer and x2 is even.

rx is even.

To prove that p is true by contrapositive method, we assume that r is false, and prove that q is also false.

Let x is not even.

To prove that q is false, it has to be proved that x is not an integer or x2 is not even.

x is not even implies that x2 is also not even.

Therefore, statement q is false.

Thus, the given statement p is true.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 11 (2018 to Current)
Chapter 14: Mathematical Reasoning
Q: 3 | Page no. 342

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Solution Show that the Following Statement is True by the Method of Contrapositive. P: If X is an Integer and X2 is Even, Then X is Also Even. Concept: Introduction of Validating Statements.
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