SET THEORY

(Source:WIKIPEDIA) Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used to define nearly all mathematical objects.

1.If A and B are two sets and A≠ B such that A∩B=A,then_______ (2)
a) A⊂B
b) B⊂A
c) both (a) and (b)
d) None of these

2.If A and B are two sets and A≠ B such that A∪B=A, then __ (2)
a) A⊂B
b)B⊂A
c) both (a) and (b)
d) None of these

3.IfA={1,2,3,4,5},B={3,5,9,6,8}then A-B is______ (1)
a) {1,2,3,4,5,6,7,8,9}
b) {1,2,4}
c) {9,6,8}
d) {3,5}

4.If A, B, C are any sets then under what condition the following statement is true.
(A-B)∪(A-C)=A (2)
a)A∩B=φ,A∩C=φ
b) A⊂B,A⊂C
c) B=C
d) None of these

5.If A and B are two sets then A’ and B’ are complements of A and B respectively then
(A∪B)’= (1)
a)A’∪B’
b) A’∩B’
c) A∪B’
d) A’∪B

6.If A and B are two sets then A’ and B’ are complements of A and B respectively then
(A∩B)’= (1)
a)A’∪B’
b) A’∩B’
c) A∩B’
d) A’∩B

7.For sets A and B, (A∩B)∪A= (1)
a) A
b) B
c) A∩B
d) None of these

8.For sets A and B, (A∩B)∩A= (1)
a) A
b) B
c) A∩B
d) None of these

9.For sets A and B, (A∪B)∪A= (1)
a) A∪B
b) B
c) A∩B
d) None of these

10.For sets A and B, (A∪B)∩A= (1)
a)A
b) B
c) A∩B
d) None of these

11.If φ is empty set and A is any set and X is universal set then A∪φ= (1)
a)A
b) φ
c) X
d) None of these

12.If φ is empty set and A is any set and X is universal set then A∩X= (1)
a) A
b) φ
c) X
d) None of these

13.If φ is empty set and A is any set and X is universal set then A∩φ= (1)
a) A
b) φ
c) X
d) None of these

14. If φ is empty set and A is any set and X is universal set then A∪X= (1)
a) A
b) φ
c) X
d) None of these

15If A’ is complement of set A, X is universal set and φ is empty set
thenA∪A’= (1)
a) A
b) φ
c) X
d) A’

16.If A’ is complement of set A, X is universal set and φ is empty set
thenA∩A’= (1)
a) A
b) φ
c) X
d) A’

17.For any threenon empty sets A, B, C, |A∪B∪C|= (1)
a) |A|+|B|+|C|+|A∩B|+|A∩C|+|B∩C|+|A∩B∩C|
b) |A|+|B|+|C|-|A∩B|-|A∩C|-|B∩C|-|A∩B∩C|
c) |A|+|B|+|C|-|A∩B|-|A∩C|-|B∩C|+|A∩B∩C|
d) |A|+|B|+|C|

18.If S = {1,2}and P(S) = {φ,{1},{2},{1,2}}then which statement is true? (1)
a) 1⊂S
b) 1∈S
c) {1}∈S
d) None of these

19.If S = {1,2}and P(S) = {φ,{1},{2},{1,2}}then which statement is true? (1)
a) {1}∈P(S)
b) φ⊂P(S)
c) φ∈P(S)
d) All are true

20.φ is empty set and A is any non empty set and X is universal set.
If A’∩X=φ then (1)
a)A=X
b) A=φ
c) A’=X
d) None of these

21.If (A∩B)’=B’ then (1)
a) A⊂B
b) B⊂A
c) A∪B=B
d) None of these

22.For any two non empty sets A and B, which statement is true ? (2)
a) A=(A-B)∪(A∩B)
b) A=(B-A)∪(A∩B)
c) A=(A-B)∪(B-A)
d) A=(A-B)∩(A∩B

23.For any two non emptysets A and B, which statement is true ? (2)
a) B=(A-B)∪(A∩B)
b) B=(B-A)∪(A∩B)
c) B=(A-B)∪(B-A)
d) B=(B-A)∩(A∩B)

24.For any non emptyset A, which statement is true ? (2)
a) A has no subset
b) A has atleast one subset
c) A has atleast two subsets
d) None of these

25.If A is a finite set of size n, the number of elements in
power set of A×A is (2)
a) 2^(2^n )
b) 〖 2〗^(n^2 )
c)2^2n
d) None of these

26.The number of elements in power set of P(S) of the set
S = {{∅},a,{b,c}} is (1)
a) 2
b) 4
c) 8
d) None of these

27.If A = {x:x^2-4x+3=0}, B = {x:x^2-3x+2=0}, C = {1,2}, D = {1,3} then (4)
a) A =C and B = D
b) A = D and B = C
c) A = D but B ≠C
d) A ≠ D but B = C

28.If A’ is complement of set A and B’ is complement of set B and
A⊂Bthen (1)
a) A’⊂B’
b) B’⊂A’
c) A^’=B’
d) None of these

29.If B’ is complement of set B and A⊂B, X is universal set then (1)
a) A∩B’=φ
b) A∩B’=X
c) A∩B’=A
d) None of these

30.If A’ is complement of set A and A⊂B, X is universal set then (1)
a) A’∪B=φ
b) A’∪B=X
c) A’∪B=B
d) A’∪B=A

  • In a survey of 60 people, it was found that 25 read newsweek magazine, 26 read time,
    26 read fortune. Also 9 read both newsweek and fortune, 11 read both newsweek and time,
    8 read both time and fortune and 8 read no magazine at all.
  1. Number of people who read all the three magazines (2)
    a) 9
    b) 8
    c) 3
    d) 11
  2. Number of people who read exactly one magazine (2)
    a) 8
    b) 10
    c) 12
    d) 30
  3. Number of people who reads fortune only (2)
    a) 8
    b) 10
    c) 12
    d) 30
  4. Number of people who reads only newsweek (2)
    a) 8
    b) 10
    c) 12
    d) 30
  5. Number of people who reads only time (2)
    a) 8
    b) 10
    c) 12
    d) 30

31. The power set of the set S = [3, {1, 4}, 5] is

A. {S, 3, 1, 4, {1, 3, 5}, {1, 4, 5} {3, 4}, Φ}

B. {S, 3, {1, 4,}, 5}

C. {S, {3}, {3, {1, 4}}, {3, 5}, Φ}

D. None of these

32. The members of the set S = {x | x is the square of an integer and x < 100} is ________________
a) {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}
b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
c) {1, 4, 9, 16, 25, 36, 64, 81, 85, 99}
d) {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}