Sasi Math (Revised for 1024)

Scroll:Theory of sets >> multiple Choice Questions: >> mcq (4165)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

If n(X) = m, n(Y) =n and n(X∩Y) = p then n(XUY) =

1) m-p
2) m-n+p
3) m+n+p
4) m+n-p

( )

If A = { 3,4,5,6} and B = { 1,2,5,6}, then AUB =

1) {1,2,5,6}
2) {3,4,5,6}
3) { 1,2,3,4,6}
4) {1,2,3,4,5,6}

( )

If U = {1,2,3,4,5,6,7,8, 9,10} and A= {2,5,6,9,10} A' is

1) ɸ
2) {1,3,5,10}
3) {2,5,6,9,10}
4) {1,3,4,7,8}

( )

If X = {a{ b, c }d}, Which of the following is subset of X

1) {a,d}
2) {b,c}
3) {a,b}
4) {c,d}

( )

If A is a proper subset of B, then A∩B =

1) AUB
2) B
3) A
4) ɸ

( )

If A = {a, b, c}, B = {e,f,g} then A∩B =

1) ɸ
2) A
3) AUB
4) B

( )

If A is a proper subset of B, then AUB =

1) ɸ
2) A
3) A∩B
4) B

( )

Which one of the following is incorrect

1) Every subset of a finite set is finite
2) Every set has a proper subset
3) Every non-empty set has at least two subsets, Æ and the set itself
4) P = { x: x-8 = - 8 } is a singleton set

( )

The number of subset of the set {10,11,12} is

1) 8
2) 6
3) 3
4) 7

( )

10)

If A = { 5,{5,6} 7,} Which of the following is correct

1) {6} € A
2) {5} € A
3) {7} € A
4) {5,6} € A

( )

If n(X) = m, n(Y) =n and n(X∩Y) = p then n(XUY) =

1) m-p
2) m+n-p
3) m-n+p
4) m+n+p

Answer: 2

SOLUTION 1 :

Hint: [n(XUY) = n(X)+n(Y) – n[(X∩Y) = m+n-p)]

ans = m+n-p

If A = { 3,4,5,6} and B = { 1,2,5,6}, then AUB =

1) { 1,2,3,4,6}
2) {1,2,3,4,5,6}
3) {1,2,5,6}
4) {3,4,5,6}

Answer: 2

SOLUTION 1 :

Ans = {1,2,3,4,5,6}

If U = {1,2,3,4,5,6,7,8, 9,10} and A= {2,5,6,9,10} A' is

1) {2,5,6,9,10}
2) ɸ
3) {1,3,5,10}
4) {1,3,4,7,8}

Answer: 4

SOLUTION 1 :

Hint: [ A" = U – A { 1,2,3,4,5,6,7,8,9,10} – {2,5,6,9,10} ={ 1,3,4,7,8}]

ans = {1,3,4,7,8}

If X = {a{ b, c }d}, Which of the following is subset of X

1) {c,d}
2) {a,b}
3) {b,c}
4) {a,d}

Answer: 4

SOLUTION 1 :

{ c,d}

If A is a proper subset of B, then A∩B =

1) ɸ
2) B
3) A
4) AUB

Answer: 3

SOLUTION 1 :

Hint: [ A∩B = set of all elements common to both A and B] A

Ans = A

If A = {a, b, c}, B = {e,f,g} then A∩B =

1) ɸ
2) A
3) AUB
4) B

Answer: 1

SOLUTION 1 :

Hint: [ A∩B ={ a,b,c,} ∩ {e,f,g} = { } = É¸]

Ans = É¸

If A is a proper subset of B, then AUB =

1) A
2) A∩B
3) B
4) ɸ

Answer: 3

SOLUTION 1 :

Hint: [ AUB = set of all elements common to both A and B]

Ans = B

Which one of the following is incorrect

1) Every non-empty set has at least two subsets, Æ and the set itself
2) Every subset of a finite set is finite
3) Every set has a proper subset
4) P = { x: x-8 = - 8 } is a singleton set

Answer: 3

SOLUTION 1 :

Hint: [ The subset of empty set Ø= { { } } . The empty set does not has a proper subset

The number of subset of the set {10,11,12} is

1) 3
2) 6
3) 7
4) 8

Answer: 4

SOLUTION 1 :

Hint: [ Number of subsets = 2^m = 2³ = 8 (Here there are three elements m = 3)]

Ans = 8

10)

If A = { 5,{5,6} 7,} Which of the following is correct

1) {7} € A
2) {5,6} € A
3) {5} € A
4) {6} € A

Answer: 2

SOLUTION 1 :

{5,6} € A