Union of Sets

Q.

The total number of subsets of a finite set $A$ has $56$ more elements than the total number of subsets of another finite set $B$. What is the number of elements in set $A$ ?

1. $5$

2. $6$

3. $7$

4. $8$

Q.

Write the given set from Roster-form to set-builder form $E=5,10,15,20$.

Q. For any three sets $A=\{1,2,3\}$
$B=\{2,3,4\},C=\{1,2,3,4,5\};A\cup B=$ $\&A\cup B\cup C=$

1. $\{1,2,3,4\}$
2. $\{1,2,3,5\}$
3. $\{1,2,3,4,5\}$
4. $\{2,3,4,5\}$

Q. Two sets are given as $X=\{10,11,12,13\}$ and $Y=\{2,3,4,6,12,18,36\},$ then $X\cup Y=$

1. $X$
2. $Y\cup X$
3. $\{2,3,4,6,10,11,12,13,18,36\}$
4. $Y$

Q.

If $A=x:x\text{is a natural number}B=x:x\text{is even natural number}C=x:x\text{is prime number}$

Then, $(A\cup B)\cap C=$

1. $A$

2. $A\cap B$

3. $B$

4. $C$

Q.

$\text{For two sets}A=\{5,6,7,8\}\&B=\{7,8,9,11\}.A\cup B=$

1. $\{5,6,7,8,9,10,11\}$

2. $\{5,6,7,8,9,11\}$

3. $\{9,11\}$

4. $\{5,6,7,8\}$

Q. The set A and set B are defined as
$A=\{x:xisanaturalnumber\}$
B = \{-x: x is a whole number\}\)
The union of set A and set B is a set of all .

1. Integers
2. Rational Numbers
3. Real Numbers
4. Integers except 0.

Q.

Match the following:

Given, U is universal set.

A, B are subsets of U.

n(U), n(A), n(B) are no. of elements in U, A, B respectively.

Number of:

(1) Elements neither in A nor in B (A) $n(A\cup B)$

(2) Elements only in A (B)$n\left(B\right)-n(A\cap B)$

(3) Elements only in B (C)$n\left(A\right)-n(A\cup B)$

(4) Elements either in A (or) in B (D)$n\left(U\right)-n(A\cup B)$

(E)$n\left(A\right)-n(A\cap B)$

1. 1 - D, 2 - E, 3 - B, 4 - A

2. 1 - D, 2 - B, 3 - E, 4 - A

3. 1 - D, 2 - C, 3 - B, 4 - A

4. 1 - D, 2 - C, 3 - A, 4 - B

Q. If $A=\{x:x\text{is an even number and}0<x<10\}$ and $B=\{2,3,5,7\}$, then the number of elements in $A\cup B$ is

Q.

If
A = {1, 2, 3, 4}

B = {3, 4, 5, 6, 7}

C = {6, 7, 8, 9}

D = {7, 8, 9, 10}

$$\begin{array}{cc}ColumnA& ColumnB\\ 1.A\cup B& a.\{3,4,6,7\}\\ 2.A\cap B& b.\varnothing \\ 3.(B\cap C)\cup D& c.\{3,4\}\\ 4.B\cup C\cup D& d.\{3,4,5,6,7,8,9,10\}\\ 5.(A\cap B)\cap (B\cup C)& e.\{1,2,3,4,5,6,7\}\\ & f.\{6,7,8,9,10\}\\ & g.\{7\}\end{array}$$

1. 1 - e, 2 - c, 3 - f, 4 -d, 5-c

2. 1 - e, 2 - c, 3 - f, 4 -d, 5-a

3. 1 - b, 2 - a, 3 - c, 4 -e, 5-f

4. 1 - b, 2 - a, 3 - c, 4 -e, 5-c