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.

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

Write the component statements of the following compound statements and check whether the compound statement is true or false. A line is straight and extends indefinitely in both directions.

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 .

Examine whether the following statements are true or false: { a, e } ⊂ { x : x is a vowel in the English alphabet}

For each of the following compound statements, first identify the corresponding component statements. Then check whether the statements are true or not. If a and b are integers, then ab is a rational number.

Write the converse and decide whether the converse is true or false. (vi) If x and y are two odd numbers, then x+y is an even number.

Write the component statements of the following compound statements and check whether the compound statement is true or false. All living things have two legs and two eyes.

By the method of contrapositive, check the validity of the statement: " If a, b in Z such that ab is odd, then both 'a' and 'b' are odd".

Write the contrapositive and converse of the following statements. If x is a prime number, then x is odd.