State whether the following statements are true or false:

- If , then
- If , then
- If Set , then A is a singleton set.
- The intelligent students of class VIII form a set.
- The students passing the half-yearly exams in Class VIII B of school is a set.
- and are overlapping sets.
- is a subset of
- If we denote the universal set as and , then
- and are disjoint sets.
- If , then where is the power set of set A.

II. If C is a letter in the word down all the subsets of C.

III. Write down the complements of all the 8 subsets of set C above.

IV. If , what is the power set of Q?

V. If , and if , and if , and if , then find : (i) (ii) (iii) (iv) (v)

VI. If , and if and if , then confirm the following: (i) the commutative property of the unions of sets B and C (ii) the commutative property of intersection of two sets A and C (iii) the associative property of the union of the sets A, B and C (iv) the associative property of intersection of sets A, B and C.

VII. If , and , and , then find (i) (ii) (iii) (iv) (v) (vi) (vii) (viii)

VIII. If , and let and let , and let , find (i) (ii) (iii) (iv) (v) (vi) Is ? (vii) Is ?

IX. All 26 customers in a restaurant had either drinks, snacks, or dinner. 18 had snacks, out of which 6 had only snacks, 4 had snacks and drinks but not dinner, 2 had drinks and dinner but not snacks, and 3 had snacks and dinner but not drinks. If 14 customers had drinks, find (i) how many customers had all three — drinks, snacks as well as dinner. (ii) how many customers had dinner but neither snacks nor drinks (iii) how many customers had only drinks.

Regards,

Nalin Pithwa