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.

State whether the following statement is true/false:For any point on the x-axis its y - coordinate is zero.

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 .

Write the component statement of each of the following statements. Also check whether the statement are true or not. i. if DeltaABC is equilateral, then it is isosceles. ii if x and y are integers, then xy is an irrational number.

Check whether the statement if x and y are odd integers, then xy is an odd integer is true or false by i. direct method ii. Contrapositive method. iii. Contradiction method.

State whether the following relations are functions or not. If it is a function check for one- to- oneness and ontoness. If it is not a function state why? If X = { x,y,z } and f= {(x,y) (x,z) (z,x) } : (f: X to X)