Cardinality of Sets

Q. In a certain code language, “ISSUE” is written as “341145”, in the same code language what will be the code for “DATES”?

1. 4567
2. 340045
3. 4120519
4. 7600

Q.

Write down the power set of set $B=\{1,2,3\}$.

Q.

If A = {1, 2, 3}, and B = {3, 6} then the number of relations from A to B is

1. 2⁶

2. 3²

3. 2 × 3

4. 2³

Q.

If $n\left(U\right)=700,n\left(A\right)=200,n\left(B\right)=300$ and $n(A\cap B)=100,$ then $n(A^{\prime }\cap B^{\prime })$ = ____.

1. 240

2. 300

3. 500

4. 400

Q.

Every set is a ___________ of itself.

Q.

What is the cardinal number of the given set?

The set of prime numbers less than $10$.

Q.

Find the cardinal number of the following sets :

(i)$A_1=\{-2,-1,1,3,5\}$

(ii)$A_2=\{x:x\in Nand3\le x<7\}$

(iii)$A_3=\{p:p\in Wand2p-3<8\}$

(iv)$A_4=\{b:b\in Zand-7<3b-1\le 2\}$ $\text{Cardinal~Number~of~set~:The number of elements in a set is called its Cardinal Number.}$

Q. The cardinality of the set A={letters of the word BANGALORE} is .

1. 8
2. 9
3. not defined

Q.

In a school, all students play either football or cricket or both. If 250 play football, 300 play cricket and 120 play both the games, then the total number of students in the school is ____.

1. 550

2. 430

3. 400

4. 500

Q. A football team won 10 matches out of the total number of matches they played. If their win percentage was 40, then how many matches did they play in all?

Q.

If A and B are disjoint sets then,

n(A U B) = ____.

1. n(A) + n(B)

2. n(A) - n(B)

3. phi

4. n(A) + n(B) - n(AB)

Q. Dividing each side of an inequation by a negative number, reverses the sign of inequality.

1. True
2. False

Q.

The cardinal number of the set A = {Present President of India} is

1. n (A) = 0

2. n (A) = 2

3. n (A) = 1

4. n (A) = 3

Q. Look at the following table:


Which of the statement is correct regarding the data represented in the table?

1. A is function of X
2. Y is a function of X
3. X is a function of Y
4. X is a function of A

Q.

If $P=\{P:Pisletterintheword"PERMANENT"\}$. Then n(P) ___.

Q.

If n(A - B) = 36, n(B - A) = 40 and n $(A\cap B)=24,$ then n $(A\cup B)=$ ___

1. A - B = {x: x ∈ A and x ∉ B}

2. The sets A - B, A ∩ B and B - A are mutually disjoint sets.

3. A - B = B - A

4. A ∪ B = {x: x ∈ B and x ∉ A}

Q. Suppose $A_1,A_2,....,A_{30}$ are thirty sets, each having 5 elements and $B_1,B_2,.....,B_n$ are n sets, each with 3 elements.
Let ${\bigcup }_{i=1}^{30}{A}_i={\bigcup }_{i=1}^n{B}_j=S$. Each element of S belongs to exactly 10 of the $A_{i}s$ and exactly 9 of the $B_{i}s$. Then n is equal to

1. 15
2. 3
3. 45
4. 50

Q.

If A and B are disjoint sets then,

n(A U B) = ____.

1. n(A) + n(B)

2. phi

3. n(A) - n(B)

4. n(A) + n(B) - n(AB)

Q. If A = {a, b, c}, then find the number of elements in the power set.

1. 32
2. 64
3. 16
4. 8

Q.

The cardinal number of the set A = {Letters of the word APPLE} is _________.

1. 5
2. 1
3. 0
4. 4

Q. Cardinal number of the set A = {x : x is an even prime number} is ____ .

1. 0

2. 2

3. 1

4. Infinite

Q. The number of elements in the set {x : x is a letter of the word 'MISSISSIPPI'}, is ____ .

1. 4

Q. If P = { x | x is a multiple of 10 } and
Q = { x | the unit’s (ones place )digit of x is not zero} then P ∩ Q is equal to .

1. P ∩ $\varphi$
2. P ∩ P
3. P

Q. If A = {a, b, c}, then find the number of elements in the power set.

1. 16
2. 8
3. 32
4. 64

Q.

If A has 3 elements and P(A) denotes the power set of A, then the number of elements in P(P(A)) is

1. 8

2. 9

3. 81

4. 256

Q. Look at the following table:


Which of the statement is correct regarding the data represented in the table?

1. X is a function of Y
2. Y is a function of X
3. A is function of X
4. X is a function of A

Q. Burst the elements of the power set of $A=\{a,b,c,d\}$.

1. {a, b, d}
2. {{}}
3. A
4. {{a, b}}
5. {{a}, {b}}
6. {{a, b, c}}
7. {}
8. {a, c, d}
9. {a, b}

Q. If A = {a, b, c, d}, then find the number of elements in the power set.

1. 8
2. 64
3. 32
4. 16

Q. Find the total numbers of subsets for set $A=\{p,q,r\}$

1. $3$
2. $6$
3. $8$
4. $4$

Q.

The cardinal number of $A=\left\{\right(x:x=5n,n\in W,n<4\}$ is ___.

1. 2

2. 5

3. 4

4. 3