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.”