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.

- Number of people who read all the three magazines (2)

a) 9

b) 8**c) 3**d) 11 - Number of people who read exactly one magazine (2)

a) 8

b) 10

c) 12**d) 30** - Number of people who reads fortune only (2)

a) 8

b) 10**c) 12**d) 30 - Number of people who reads only newsweek (2)
**a) 8**b) 10

c) 12

d) 30 - 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}