Check whether the following statement is true or not: p : If x and y

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

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

Answer»

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.”