Combine the following pair of statements using “if and only if”.
(i) p : If a rectangle is a square, then all its four sides are equal.
    q : If all the four sides of a rectangle are equal, then the rectangle is a square.

(ii) p : If the sum of digits of a number is divisible by 3, then the number is divisible by 3.
     q : If a number is divisible by 3, then sum of its digits is divisible by 3.

Show that the statement “For any real numbers a and b, a² = b² implies a = b” is not true by giving a counter - example.

Given below the two statements
p : 25 is a multiple of 5.
q : 25 is a multiple of 8.
Write the compound statements connecting these two statements with “And” and “Or”. In both the cases, check the validity of the compound statement.

Check the validity of the statement given below by contradiction method.
p : The sum of an irrational number and a rational number is irrational.

Verify by method of contradiction that  is irrational.

Which of the following are statements? Justify your answer.
(i) The set of prime integers is infinite.
(ii) Paris is in England.
(iii) May God bless you !
(iv) The number x is a positive integer.
(v) How far is Dubai from here ?
(vi) x + 2 = 9.

Determine whether the following compound statements are true or false.
(i) Delhi is in India and 2 + 2 = 4.
(ii) Delhi is in England and 2 + 2 = 4.