State whether the "OR" used in the following statements is "exclusive" or "inclusive". Give reasons for your answer.

(i) Sun rises or moon sets.

(ii) To apply for a driving license, you should have a ration card or a passport.

(iii) A lady gives birth to a baby boy or baby girl.

(iv) All integers are positive or negative.

Identify the quantifier in the following statements and write the negation of the statements.

(i) There exists a number which is equal to its square.

(ii) For every real number x, x is less then x + 1.

(iii) There exists a capital for every state in India.

Check whether the following pair of statements is negation of each other. Give reasons for your answer.

(i) x + y = y + x is true for every real number x and y.

(ii) There exists a real number x and y for which x + y = y + x.

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.

Write the contra positive and converse of the following statements.

(i) If x is a prime number, then x is odd.

(ii) If the two lines are parallel, then they do not intersect in the same plane.

(iii) Something is cold implies that it has low temperature.

(iv) You cannot comprehend geometry if you do not know how to reason deductively.

(v) x is an even number implies that x is divisible by 4