Check whether the following statement is true or not: If `x\ a n d\ y` are odd integer, then `x y` is an odd integer.

Explanation

Let `p :x,yin Z` such that x and y are odd.
`q:` xy is odd.
from rule 3,
Let p is true then `x==2m+1`, for some integer m
`y=2n+1`, for some integer n
`thereforexy=(2m+1)(2n+1)`
`=4mn+2m+2n+1`
`=2(2mn+m+n)+1`
`rArrxy` is odd.
`therefore` q is true.
Therefore, 'if p then q' is a true statement.