Question

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 1

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.”