Question 1:
Find the cardinal number of the following sets.
(i) M = {p, q, r, s, t, u}
(ii) P = {x : x = 3n + 2, n∈W and x < 15}
(iii) Q = { y : y = 4/3n, n ∈ N and 2 < n ≤ 5}
(iv) R = {x : x is an integers, x ∈ Z and –5 ≤ x < 5}
(v) S = The set of all leap years between 1882 and 1906.
Question 2 :
Identify the following sets as finite or infinite.
(i) X = The set of all districts in Tamilnadu.
(ii) Y = The set of all straight lines passing through a point.
(iii) A = { x : x ∈ Z and x < 5}
(iv) B = {x : x^{2}–5x+6 = 0, x ∈N}
Question 3 :
Which of the following sets are equivalent or unequal or equal sets?
(i) A = The set of vowels in the English alphabets.
B = The set of all letters in the word “VOWEL”
(ii) C = {2, 3, 4, 5}
D = { x : x ∈ W, 1 < x < 5}
(iii) E = The set of A={ x : x is a letter in the word “LIFE”}
F = {F, I, L, E}
(iv) G = {x : x is a prime number and 3 < x < 23}
H = {x : x is a divisor of 18
Solution
Question 4 :
Identify the following sets as null set or singleton set.
(i) A = {x : x ∈N, 1 < x < 2}
(ii) B = The set of all even natural numbers which are not divisible by 2
(iii) C = {0}.
(iv) D = The set of all triangles having four sides.
Solution
Question 5 :
State which pairs of sets are disjoint or overlapping?
(i) A = {f, i, a, s} and B={a, n, f, h, s}
(ii) C = {x : x is a prime number, x >2} and D ={x:x is an even prime number}
(iii) E = {x : x is a factor of 24} and F={x : x is a multiple of 3, x < 30}
Solution
Question 6 :
If S = {square, rectangle, circle, rhombus, triangle}, list the elements of the following subset of S.
(i) The set of shapes which have 4 equal sides.
(ii) The set of shapes which have no sides.
(iii) The set of shapes in which the sum of all interior angles is 180^{o}
(iv) The set of shapes which have 5 sides.
Solution
Question 7 :
If A = {a, {a, b}}, write all the subsets of A.
Solution
Question 8 :
Write down the power set of the following sets.
(i) A = {a, b}
(ii) B = {1, 2, 3}
(iii) D = {p, q, r, s}
(iv) E = ∅
Question 9 :
Find the number of subsets and the number of proper subsets of the following sets.
(i) W = {red, blue, yellow}
(ii) X = { x^{2} : x ∈ N, x^{2} ≤ 100}
Question 10 :
If n(A) = 4, find n [P(A)].
(ii) If n(A) = 0, find n [P(A)].
(iii) If n[P(A)] = 256, find n(A).
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