If m is an even integer, show that `m^(2)` is also an even integer.

If n is an odd integer, prove that n^(2) is also an odd integer.

Check whether the follwing compound statements is true or false . If a and b are odd integers , then (a +b) is an even integer .

‘If a and b are two odd integer, then (a + b) is an even intege.”—examine whether this compound statement is true of false

Show that ((sinA+sinB)/(cosA+cosB))^(n) + ((cosA-cosB)/(sinA-sinB))^(n) = 2 "tan"^(n) (A+B)/2 when n is an even integer, 0, when n is an odd integer.

Using contrapositive method show tha the compund statement .is true or not. If x and y are odd integers,'then xy is also a odd integer.

If x and y are odd integers, then xy is also an odd integer r examine its truth value.

If f(x)=x^m n ,n in N , is an even function, then m is even integer (b) odd integer any integer (d) f(x)-e v e ni snotpos s i b l e

If n is a positive integer, show that, in the expansion of (1+x)^(n) the sum of the coefficents of terms in the odd positions is equal to the sum of the cofficients of term in the even positions and each sum is equal to 2^(n-1) .

Which of the following pairs of sets are disjoint { x : x is an even integer } and { x : x is an odd integer}

Find the probability that an even integer chosen at random from first 400 positive integers is divisible by 5 or 7?