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Show that the following statement is …

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Show that the following statement is grue by the methord by contrapositive "If x is an integer and x^is even then x is also even
  • 1 answers

Gaurav Seth 5 years ago

The component statements of given statement are:
q : x is an integer and x2  is even
r : x is an even integer.
In method of contrapositive,
We assume that ~r is true and we have to prove that ~q is also true.
Now, ~r is true,
Therefore, x is not an even integer or x is an odd integer.

or x = 2n + 1 for some integer n.
or 
or 
or 
or  is an odd integer.
or q is false.
or ~q is true.
Thus, 
Hence, the given statement p is true.

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