
1. If U = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U.
A = {0}
C = {1, 9, 5, 13}
D = {5, 11, 1}
E = {13, 7, 9, 11, 5, 3, 1}
F = {2, 3, 4, 5}
2. Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) C = {2, 4}.
(a) B __ A
(b) C __ A
(c) B __ C
(d) ∅ __ B
(e) C __ C
(f) C __ B
3. Which of the following sets is a universal set for the other four sets?
(a) The set of even natural numbers
(b) The set of odd natural numbers
(c) The set of natural numbers
(d) The set of negative numbers
(e) The set of integers
4. Write all the subsets for the following.
(a) {3}
(b) {6, 11}
(c) {2, 5, 9}
(d) {1, 2, 6, 7}
(e) {a, b, c}
(f) ∅
(g) {p, q, r, s}
5. Write down all the possible proper subsets for each of the following.
(a) {a, b, c, d}
(b) {1, 2, 3}
(c) {p, q, r}
(d) {5, 10}
(e) {x}
(f) ∅
(a) containing 3 elements
(b) whose cardinal number is 5
7. Find the number of proper subsets of a set
(a) containing 6 elements
(a) containing 6 elements
(b) whose cardinal number is 4
8. Show with an example that if the number of elements in a set is ‘n’, then
(a) the number of subsets is 2n
(b) the number of proper subsets is 2n - 1.
9. Write the universal set for the following.
(a) P = {4, 6, 8} Q = {1, 3, 9} R = {0, 2, 5} S = {7}
(b) X = {a, b, c} Y = {c, b, f} Z = {e, g}
(c) Prime numbers less than 10, even numbers less than 10, multiples of 3 less than 10.
10. If ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 4, 6, 8}
B = {3, 5, 7}
C = {1, 5, 7, 8, 9}
Find (a) A’ (b) B’ (c) C’
11. State whether true or false.
(a) Quadrilateral ⊆ polygon
(b) {1} ↔ {0}
(c) Whole numbers ⊆ natural numbers
(d) {a} ∈ {d, e, f, a}
(e) Natural numbers ⊆ whole numbers
(f) Integers ⊆ natural numbers
(g) 0 ∈ ∅
(h) ∅ ∈ {1 , 2, 3 }
13. Let A {x : x = n — 2, n < 5}. Find A when
(a) n = W, n ∈ W
(b) n = N, n ∈ N
(c) n ∈ I = I
14. If U = {2, 3, 4, 5, 6, 7, 8, 9} X = {3, 5, 7, 9} Y = {2, 4, 6, 8}
Show that X = Y’ and Y = X’
15. Let P = {3, 5, 7, 9, 11} Q = {9, 11, 13} R = {3, 5, 9} S = {13, 11}
Write Yes or No for the following.
(a) R ⊂ P
(b) Q ⊂ P
(c) R ⊂ S
(d) S ⊂ Q
(e) S ⊂ P
(f) P ⊄ Q
(g) Q ⊄ R
(h) S ⊄ Q
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