Intersection

Q.

If A and B are any two sets, then $A\cup (A\cap B)$ = ___.

1. $A^C$

2. $B^C$

3. B

4. A

Q.

The area of the circle whose centre is at (1, 2) and which passes through the point (4, 6) is

1. None of these
2. 
3. 
4. 

Q.

If A=(2, 4) and B=[3, 5), find $A\cap B$.

Q.

If A, B and C be three non empty sets given in such a way that $A\times B=A\times C$, then prove that B = C.

Q.

Which of the following relations is not a function?

1. R={(1, 2), (1, 4)(3, 1), (5, 1)}

2. R= {(2, 1), (4, 4)(3, 1), (5, 1)}

3. R= {(1, 2), (3, 4)(2, 1), (5, 2)}

4. R= {(1, 2), (3, 4), (2, 1), (5, 1)}

Q.

If A and B are two sets containing 3 and 6 elements respectively, what can be the maximum number of elements in $A\cup B$?
Find also the minimum number of elements in $A\cup B$

Q.

If $(A\cup B)=(A\cap B)$ then prove that A=B

Q.

Write the set $C=\{2,4,8,16,32\}$ in the set-builder form.

Q.

If A = {x: x is a prime number}

B = {x: x is an odd natural number}

Then A ∩ B is

1. None of these

2. {3, 5, 7, 11, 13, 17, .....}

3. {2, 3, 5, 7, 9, 11, .....}

4. {1, 3, 5, 7, 11, 13, 17, .....}

Q. Show that the following four conditions are equivalent: (i) A ⊂ B (ii) A – B = Φ (iii) A ∪ B = B (iv) A ∩ B = A

Q.

Let n(U) = 700, n(A) = 200, n(B) = 300 and n(A ∩ B) = 100,

Then n($A^c$ ∩ $B^c$ =

1. 400

2. 600

3. 300

4. 200

Q. If A = {x: x = 2n+1, n ∈ N and 3 ≤ n ≤ 9}, then the cardinality of A is .

1. 3
2. 9
3. 7
4. 6

Q. If $f\left(x\right)+f(x+4)=f(x+2)+f(x+6)\forall xϵRanda>0$ and f(x) is periodic, then period of f(x), is

1. 1000
2. 100
3. 10000
4. 10

Q. Find the domain of the function $f\left(x\right)=\frac{x^2+2x+1}{x^2-8x+12}$

Q. 10. IfX= { a, b, C, d } and Y= {f, b, d, g}, findi) Y -X(ii) XnY

Q.

Let N be the universal set.
(i) if A={$x:xϵN$ and x is odd} find A'

(ii) if B={$x:xϵN$, x is divisible by 3 and 5 } find B'

Q.

If B $\times$ A = {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c), (z, a), (z, b), (z, c)} Find set A and set B.

1. C = (b, z, x) B = (c, b, y)

2. A = (a, x, y) B = (b, c, z)

3. A = (x, y, z) B = (a, b, c)

4. A = (a, b, c) B = (x, y, z)

Q. 11. Let a, ={1, 2, 3, 4, 5}, b={2, 3, 6, 7}. Then the number of elements in (ab)intersection(ba)

Q. If $A=\{x:x=2k,k\in N\text{and}k\le 100\}$, $B=\{x:x=2^k,k\in W\text{and}k<11\}$ and $C=\{x:x=k^3,k\in N\text{and}k<11\}$, then the value of $n\left(A△B\right)+n\left(B△C\right)+n\left(A△C\right)$ is

1. $220$
2. $216$
3. $203$
4. $207$

Q.

$If{x}^2+2ax+a<0forallxϵ[1,2]then:$

1. 

2. 

3. 

4. 

Q. In a factory, 70% of the workers like oranges and 64% likes apples. is the minimum percentage possible for workers who like both.

1. 30
2. 34
3. 6
4. 36

Q.

For any sets A and B, prove that

$(A\times B)\cap (B\times A)=(A\cap B)\times (B\cap A)$.

Q.

If A and B are two sets containing 3 and 6 elements respectively, what can be the maximum number of elements in $A\cup B$ ?

Also, find hte minimum number of elements in $A\cup B$

Q.

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A UB

1. 18

2. 9

3. 6

4. 3

Q.

Divide $4x^3+12x^2+11x+3byx+1$ and then find the quotient.

1. $2x^2+3x+3$

2. $4x^2+6x+1$

3. 

4. $8x^2+11x+3$

Q. Let A and B be two sets having 4 and 7 elements respectively. Then write the maximum number of elements that $A\cup B$ can have.

Q.

If A = {x: $x^2$ - 5x + 6 = 0}, B = {2, 4} , C = {4, 5}, then

A×(B $cap$ C) is

1. {(4, 2), (4, 3)}

2. {(2, 4), (3, 4), (4, 4)}

3. {(2, 2), (3, 3), (4, 4), (5, 5)}

4. {(2, 4), (3, 4)}

Q.

If sets A and B are defined as
$A=\left\{\right(x,y)|y=\frac{1}{x},x\ne 0,xϵR\},B=\left\{\right(x,y)|y=-x,xϵR\}$, then

1. $A\cup B=B$

2. $A\cap B=\varphi$

3. $A\cup B=A$

4. $A\cap B=A$

Q. Show that A ∩ B = A ∩ C need not imply B = C.

Q. Let $f,g$ : $R\to R$ be defined respectively by $f\left(x\right)=x+1,g\left(x\right)=2x-3$. Find $f+g,f-g$ and $\frac{f}{g}$