Question
Show that the following statement is true by the method of contrapositive
p : If is an integer and is even then is also even
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Text solutionVerified
: If is an integer and is even then is also even.
Let : is an integer and is even
: is even
To prove that is true by contrapositive method we assume that is false and prove that is also false.
Let is not even
To prove that is false, it has to be proved that is not an integer or is not even.
is not even implies that is also not even.
Therefore statement is false.
Thus the given statement is true.
Let : is an integer and is even
: is even
To prove that is true by contrapositive method we assume that is false and prove that is also false.
Let is not even
To prove that is false, it has to be proved that is not an integer or is not even.
is not even implies that is also not even.
Therefore statement is false.
Thus the given statement is true.
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Question Text | Show that the following statement is true by the method of contrapositive p : If is an integer and is even then is also even |
Answer Type | Text solution:1 |
Upvotes | 150 |