Exercise 1.2: Types of Sets

Exercise 1.2

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.

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 : x²–5x+6 = 0, x ∈ ℕ }

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) X= { x : x is a letter in the word “LIFE”}

Y={F,I,L,E}

(iv) G= { x : x is a prime number and 3 < x < 23}

H = { x : x is a divisor of 18}

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.

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}

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 radius.

(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.

7. If A = {a, {a, b}}, write all the subsets of A.

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 = ∅

9. Find the number of subsets and the number of proper subsets of the following sets.

(i) W = {red, blue, yellow}

(ii) X = { x² : x ∈ ℕ , x² ≤ 100}.

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).