Find the component statements of the following compound statements:

(i) The sky is blue, and the grass is green.

(ii) The earth is round, or the sun is cold.

(iii) All rational numbers are real, and all real numbers are complex.

(iv) 25 is a multiple of 5 and 8.

The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the following events:

A = The number on the first slip is larger than the one on the second slip.

B = The number on the second slip is greater than 2

C = The sum of the numbers on the two slips is 6 or 7

D = The number on the second slips is twice that on the first slip.

Which pair (s) of events is (are) mutually exclusive?

A card is picked up from a deck of 52 playing cards.

(i) What is the sample space of the experiment?

(ii) What is the event that the chosen card is a black faced card?

For each of the following statements, determine whether an inclusive “OR” o exclusive “OR” is used. Give reasons for your answer.

(i) Students can take Hindi or Sanskrit as their third language.

(ii) To entry a country, you need a passport or a voter registration card.

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

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

Write the component statements of the following compound statements and check whether the compound statement is true or false:

(i) To enter into a public library children need an identification card from the school or a letter from the school authorities.

(ii) All rational numbers are real and all real numbers are not complex.

(iii) Square of an integer is positive or negative.

(iv) x = 2 and x = 3 are the roots of the equation 3x² – x – 10 = 0.

(v) The sand heats up quickly in the sun and does not cool down fast at night.