Page 82 - ICSE Math 8

6. If K = {5, 10, 15, 20, 25}, L = {10, 20, 30, 40}, M = {4, 8, 12, 16, 20, 24} and
P = {8, 10, 12, 14, 16, 20, 24} then find:
(a) K – L (b) M – P (c) P – K (d) L – M (e) K – P
7. If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?
8. If U = Set of even natural numbers between 10 and 30, A = {12, 16, 18, 22, 26} and
B = {14, 16, 18, 20, 24, 28}, verify that:
(a) (A ∪ B)′ = A′ ∩ B′ (b) (A ∩ B)′ = A′ ∪ B′
9. If U = {x : x is a letter of the word COMMUNICATION}. Find the complement of the following sets.
(a) A = {M, U, T, A} (b) B = {O, C, I, N} (c) C = {T, I, A, N, M} (d) D = {C, U, N}
10. If U = {x : x is a month of a year}, A = {x : x is a month with 30 days},
B = {x : x is a month with 31 days}, C = {x : x is a month starting with the letter J}

D = {x : x is a month starting with the letter A}, then write sets U, A, B, C and D in roster form and find
the following sets.
(a) A ∩ C′ (b) B′ (c) A ∩ (C ∪ D)
(d) B ∩ D′ (e) B ∩ (C ∪ D) (f) C′ ∪ D′

AT A GLANCE
¾ A set is a collection of well-defined and distinct objects.

¾ A set which has countable number of elements is called a finite set, otherwise it is an infinite set.
¾ A set which contains only one element is called a singleton set.
¾ A set which does not have any element is called a null set.
¾ Two sets are said to be equal if they have the same elements and they are called equivalent if they have
the same number of elements.

¾ Two sets are said to be disjoint if they do not have any element in common.
¾ Two sets are said to be overlapping if they have at least one element in common.
¾ The number of elements present in a finite set is called the cardinal number of that set.
¾ If all elements of set A are in set B, then A ⊆ B.
¾ Union of two sets A and B is the set of all the elements that are either in A or in B or in both.
¾ Intersection of two sets A and B is the set of elements common to both A and B.
¾ A – B is the set of elements which belong to A but not to B.
¾ B – A is the set of elements which belong to B but not to A.
¾ The complement of a set is defined as the set of those elements of the universal set which are not in the
given set.

MENTAL MATHS

1. Match the following.
2
(a) {x : x is an integer and x – 4 = 0} (i)   2 4 68  , ,, 
 4 5 67 
(b) {x : x is a letter of the word PICNIC} (ii) {April, June, September, November}
2n
(c) {x : x = , n ∈ N, n < 5} (iii) {P, I, C, N}
n + 3
(d) {x : x is a month of a year with 30 days} (iv) {–2, 2}

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