Q. 2 A5.0( 1 Vote )

# Check whether the following statement is true or not:p : If x and y are odd integers, then x + y is an even integer.

Let us Assume that p and q be the statements given by

p: x and y are odd integers.

q: x + y is an even integer

since the given statement can be written as :

if p, then q.

Let p be true . then,

x and y are odd integers

x = 2m+1, y = 2n+1 for some integers m,n

x+y = (2m+1)+(2n+1)

x+y = (2m+2n+2)

x+y = 2(m+n+1)

x + y is an integer

q is true.

Therefore, p is true q is true

Hence, “if p, then q “ is a true statement.”

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