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

Check whether the following statement is true or false by proving its contrapositive. If x, y in Ζ such that xy is odd, then both x and y are odd.

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

State whether the following statement is true or false : If x, y both are functions of t, then (d^(2)y)/(dx^(2))=((d^(2)y)/(dt^(2)))/((d^(2)x)/(dt^(2))).

Check whether the following statement is true or false by proving its contrapositive. 'If x,y are integers such that xy is odd, then both x and y are odd integers'.

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.

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

Check whether the following pair of statements are negation of each other. Give reasons for your answer x + y = y + x is true for every real numbers x and y. There exists real numbers x and y for which x + y = y + x.

State whether the following statements are true or false. Give reasons for your answers. Square number can be written as the sum of two odd numbers .

By giving a counter example show that the following compound statement is not true . "If x and y are two real numbers , then x^(2)=y^(2) implies x = y " .

Let a statement p : DeltaABC is a right angled triangle and another statement q : In a DeltaABC,AB^(2)+BC^(2)=AC^(2). Check whether the following statements are true or false . p is true if and only id q is true