Using direct method prove that if `x, y in N` and `x,y` are odd then xy is also odd.

Using contrapositive method prove that if n^(2) is an even integer, then n is also an even integers.

Prove that if x is odd , then x^(2) is also odd.

Check whether the following statement is true or not: If x,y in Z are such that x and y are odd, then xy is odd.

Which of the following statements are true and which are false? s: If x and y are odd then xy is odd.

Using the method of integration find the area of the region bounded by lines : 2x + y =4 , 3x - 2y = 6 and x-3y +5=0 .

Prove by direct method that for any real numbers x,y if x=y , then x^(2)=y^(2)

Using the method of integration find the area bounded by the curve |x|+|y|= 1. [Hint: The required region is bounded by lines x + y = 1, x - y = 1, -x + y = 1 and -x -y =1].

Rewrite the following statement with “if-then” in five different ways conveying the same meaning. If a natural number is odd, then its square is also odd.

If n is odd then n^2 is odd ' compound statement is false .