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.

Which one of the following is incorrect

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

( )

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

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

( )

Which of following statements are true

(i) For any set A, A is a proper subset of A.

(ii) For any set A, ɸ is a subset of A.

(iii) For any set A, A is a subset of A.

1) (i),(ii) and (iii)
2) (i) and (iii)
3) (i) and (ii)
4) (ii) and (iii)

( )

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

1) A∩B
2) A
3) B
4) ɸ

( )

The number of elements of the set { x ; x € Z, x² = 1 } is

1) 1
2) 2
3) 0
4) 3

( )

Which one of the following is a finite set

1) {x : x € Z, x < 5 }
2) {x : x is an even prime number}
3) { x : x € W, x ≥ 5}
4) 10} ' title="{x : x € N, x > 10} "/> {x : x € N, x > 10}

( )

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

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

( )

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

1) AUB
2) ɸ
3) A
4) B

( )

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

1) A
2) ɸ
3) B
4) AUB

( )

10)

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

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

( )

Which one of the following is incorrect

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

Answer: 1

SOLUTION 1 :

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

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

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

Answer: 3

SOLUTION 1 :

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

Which of following statements are true

(i) For any set A, A is a proper subset of A.

(ii) For any set A, ɸ is a subset of A.

(iii) For any set A, A is a subset of A.

1) (i),(ii) and (iii)
2) (ii) and (iii)
3) (i) and (iii)
4) (i) and (ii)

Answer: 2

SOLUTION 1 :

(ii) and (iii)

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

1) B
2) A
3) A∩B
4) ɸ

Answer: 1

SOLUTION 1 :

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

Ans = B

The number of elements of the set { x ; x € Z, x² = 1 } is

1) 1
2) 3
3) 2
4) 0

Answer: 3

SOLUTION 1 :

ans = 2

Hint: [ { x : x € Z, x² = 1} = { -1, 1}]

Which one of the following is a finite set

1) { x : x € W, x ≥ 5}
2) {x : x is an even prime number}
3) 10} ' title="{x : x € N, x > 10} "/> {x : x € N, x > 10}
4) {x : x € Z, x < 5 }

Answer: 2

SOLUTION 1 :

Hint: [{ x : x is an even prime number} = {2}, which is finite]

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

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

Answer: 3

SOLUTION 1 :

{5,6} € A

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

1) B
2) ɸ
3) A
4) AUB

Answer: 2

SOLUTION 1 :

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

Ans = É¸

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

1) A
2) ɸ
3) B
4) AUB

Answer: 1

SOLUTION 1 :

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

Ans = A

10)

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

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

Answer: 2

SOLUTION 1 :

{ c,d}