TYPES OF SETS WORKSHEET

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.

Solution

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 : x²–5x+6 = 0, x ∈N}

Solution

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 = ∅         

Solution

Question 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} 

Solution

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).  

Solution

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