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Check Whether the Statement Are True Or Not: P : If X and Y Are Odd Integers, Then X + Y is an Even Integer. - Mathematics

Check whether the statement are true or not: 

p : If x and y are odd integers, then x + y is an even integer.

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Solution

 p: If x and y are odd integers, then x + y is an even integer.
Let q and r be two statements.
Here,
qx and y are odd integers.
rx + y is an even integer.
Let q be true.
Then, q is true.
Now,
x and y are odd integers.
x = 2m +1 and = 2n + 1 for some integers and n.

⇒ x y = (2m + 1) + (2n + 1)

⇒ x + y = 2m + 2n + 2 = 2(m + n + 1)
So, x + y is an even integer.
Hence, the statement is true.

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 31 Mathematical reasoning
Exercise 31.6 | Q 2.1 | Page 28
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