Complement of a Set

Q. Let A = {x : x is an even natural number and 1< x $\le$ 12} and
B = { x : x is a multiple of 3, x $ϵ$ N and x $\le$ 12} be two sets. Find A $\cap$ B. Are both sets disjoint?

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 number of students who play football only are ___.

1. 180

2. 130

3. 150

4. 120

Q. Verify whether A = {20, 22, 23, 24} and B = {25, 30, 40, 45} are disjoint sets.

Q.

Question 78

Divide $\frac{3}{10}$ by $\left(\frac{1}{4}of\frac{3}{5}\right)$

Q. If $A$ = {1, 3, 5, 7, 9, 11, 13, 15, 17}, $B$ = {2, 4, 6, 8, 10, 12, 14, 16, 18} and $N$ the set of natural numbers is the universal set, then $A^{\prime }\cup \left(\right(A\cup B)\cap B^{\prime })$ is:

1. $\varphi$
2. $N$
3. $A$
4. $B$

Q.

Question 2 (iv)

Find
33.1 $÷$ 10

Q. Question 3 (v)
Find
31.1 $\times$ 100

Q.

If ∪ = {2, 4, 6, 8, 10, 12, 14, 17}, where ∪ is Universal set

and some set A = {1, 4, 6, 9, 11, 12}

The set A^C is

1. {1, 2, 8, 10, 14, 17}

2. {2, 8, 10, 14, 17}

3. Can't be determined

4. {2, 8, 10, 14, 17}

Q. If $U=\{1,2,3,4,5\}$ and $A=\{2,5\}$, then $A^{\prime }=$

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

Q.

Question 42

State whether the following statement is true (T) or false (F).

If $\frac{15}{8}-7x=9,$ then $-7x=9+\frac{15}{8}.$

Q. Question 7(i)
Find
$\frac{1}{2}of\left(i\right)2\frac{3}{4}\left(ii\right)4\frac{2}{9}$

Q.

If a universal set $U=\{3,4,5,6,7,8,9,10,11,12\}A=\{4,6,8,10,12\}B=\{3,5,7,9,11\}$ then $(A\cup B{)}^{\prime }$ is

1. $\varnothing$

2. $\{3,4\}$

3. $\{5,6,7,8\}$

4. $\{9,10,11,12\}$

Q.

Question 2 (iii)

Find
0.7 $÷$ 10

Q.

Question 1 (iv)

Which of the drawings (a) to (d) show:
$3\times \frac{1}{4}$
a)

b)

c)

d)

Q. Question 1 (v)
$\frac{7}{10}+\frac{2}{5}+\frac{3}{2}$

Q.

Question 5 (i)
Find
7 $÷$ 3.5

Q. Question 5 (ii)
Find
36 $÷$ 0.2

Q. Question 9
7x -9 =16

Q.

The number of ways in which the letters of the word $\text{ARRANGE}$ can be arranged such that both $\text{R}$ do not come together is?

1. $360$

2. $900$

3. $1260$

4. $1620$

Q. If a universal set $U=\{1,2,3,4,5,6,7,8,9,10\},A=\{2,4,6,8,10\},andB=\{1,3,5,7,9\}$, find the value of $(A\cup B{)}^{\prime }$.

Q. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, C = {3, 4, 5, 6} then prove the following :
A' = {5, 6, 7, 8, 9}

Q. $|x|$ represent number of elements in region X. Now the following conditions are given
$|U|=14$, $|(A-B{)}^C|=12$, $|A\cup B|=9$ and $|A\Delta B|=7$, where A and B are two subsets of the universal set U and $A^C$ represents complement of set A, then?

1. $|A|=2$
2. $|B|=5$
3. $|A|=4$
4. $|B|=7$

Q. If $n(\cup )=900$, $n\left(A\right)=300$, $n\left(B\right)=200$, $n(A\cap B)=100$, then find $n(A^{{}^{\prime }}\cap B^{{}^{\prime }})$.

Q.

U = {x: x is a natural number and x ≤ 10}
$\text{A = {a : a is an even natural number and a < 10}}$

B = {b : b is a prime number and b ≤ 9}

What is the value of A^I ∩ B^I?

Q.

Write the given set from Roster-form to set-builder form $D=\left\{1,4,9,16,25\right\}.$

Q. Universal set $\text{U}=\{x:x\text{is an even natural number and}$$x<15\}$
If $\text{A}=\{x:x=4n,x\le 12\text{and}n\in \text{N}\}$, then ${\text{A}}^{\prime }$ is:

1. $\{4,8,12\}$
2. $\{2,4,6,8,10,12\}$
3. $\{1,3,5,7,9,11,13\}$
4. $\{2,6,10,14\}$

Q.

Question 165

Find two repeater machines that will do the same work as a $(\times 81)$ machine.

Q. Write the set $A=\{1,4,9,16,........\}$ in set builder form.

Q.

If $S=\{2,4,6,8,10,12\}$ and $A=\{4,8,12\}$, find $A^{\prime }$.

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. 400

2. 600

3. 300

4. 200