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 180o

(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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