1. Which of the following are sets?
(a) The collection of all real numbers less than 400. (c) The collection of intelligent students.
(b) The collection of honest persons. (d) The collection of all even integers.
2. Describe the following set in Roster form:
(a)
A x :x 32 and x N (b)
3
A x : x 27 0 ¡ (c)
A x : 3 x 3 and x
3. Write down the power set of the following sets: (a)
1, 2 (b)
1, 2,8 (c) {a, e, i, o}
4. If
0,3Gthen construct the sets : (a)
P G (b)
G P G (c)
G P G
5. If
0,1, 2,3 , 0, 2,3, 4, 7 & 2, 4, 5,7, 8 A B C then find
(i) A B (ii) A B (iii) A B (iv) B A (v) A B (vi)
A B C
(vii)
A B C (ix)
C B A (x)
C B A (xi)
A B C (xii) B C
6. If
0,1, 2,3, 4, 5,6, 7, 8 , 3, 4, 7 , 2, 7,8 & 0,1,5, 8 U A B C then verify;
(i)
A B C A B C (ii)
A B C A B C
(iii)
A B C A B A C (iv)
A B C A B A C
7. If
0,1, 2, 3, 4, 5, 6U,
0,1, 2, 3Aand
0, 2 , 3, 5Bthen find
(a)
C
A B (b)
C
B A (c)
C
U A B (d)
A A B
8. If k
A [1,2,......k], where k N , then find
5
1 2 3 7 1 4 i
i 2
(i)A A (ii)A A (iii)A A (iv) A
9. Given N {x : x is a natural number}; A {x : x N & x is multiple of 2}
B {x : x N & x is multiple of 5}; C {x : x N & x is multiple of 3} Find
(i)
A B C (ii)
( ) A B C iii A B A C (iv)
A B C (v)
A B C
10. State and prove De Morgan’s law.
11. Shade the following sets in the Venn diagram in fig 1.0:
(a)
C
A B (b)
C
B A (c)
C
A B C
(d)
C
A B C (e)
A B C (f)
A B C
1. In a group of 850 persons, 600 can speak English and 340 can speak Hindi. Find:
(a) How many speak Hindi only? (b) How many speak English only? (c) How many speak both languages?
2. In a group of 100 persons, 50 drink tea but not coffee, 70 drink tea and 10 drink neither tea not coffee.
Find: (a) How many drink both tea and coffee? (b) How many drink coffee? (c) How many drink coffee but not tea?
3. If A and B are two non-empty sets such that
40n A ,
60 n A B and
10 n A B . Find
n B .
4. If A and B are two non-empty sets such that
8n A ,
18 n A B and
15n B . Find
n A B .
5. In a survey of 100 persons it was found that 28 read newspaper A, 30 read newspaper B, 42 read newspaper C, 8 read
newspaper A and B, 10 read newspaper A and C, 5 read newspaper B and C and 3 read all newspapers. Find:
(a) How many read neither of three? (b) How many read newspaper C only?
6. Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets
of the second set. Find the values of m and n.
