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Question
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,
q: x and y are odd integers.
r: x + y is an even integer.
Let q be true.
Then, q is true.
Now,
x and y are odd integers.
x = 2m +1 and y = 2n + 1 for some integers m 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.
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