# Union

## Trending Questions

**Q.**

A survey shows that $73\%$ of the persons working in an office like coffee, whereas $65\%$ like tea. If $x$ denotes the percentage of them, who like both coffee and tea, then $x$ cannot be:

$63$

$54$

$38$

$36$

**Q.**

In a group of 65 people 40 like cricket, 10 like both cricket and tennis, how like tennis only and not cricket?

**Q.**

For any two sets A and B, prove that

(i) B⊂A∪B

(ii) A∩B⊂A

(iii) A⊂B⇒A∩B=A

**Q.**

Let $\mathrm{n}\left(\mathrm{U}\right)=700,\mathrm{n}\left(\mathrm{A}\right)=200,\mathrm{n}\left(\mathrm{B}\right)=300$ and $\mathrm{n}(\mathrm{A}\cap \mathrm{B})=100$, then $n({\mathrm{A}}^{\mathrm{c}}\cap {\mathrm{B}}^{\mathrm{c}})=$

$400$

$600$

$300$

$200$

**Q.**

Let $A$ and $B$ be the two sets such that $n\left(A\right)=0.16$, $n\left(B\right)=0.14$, $n\left(A\cup B\right)=0.25$.Then $n\left(A\cap B\right)$ is equal to

$0.3$

$0.5$

$0.05$

None of these

**Q.**

The value of $(A\cup B\cup C)$ intersection ( $A$ intersection ${B}^{C}$ intersection ${C}^{C}$)${}^{C}$ intersection ${C}^{C}$ is,

$B\cap {C}^{C}$

${B}^{C}\cap {C}^{C}$

$B\cap C$

$A\cap B\cap C$

**Q.**

If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A × B)?

**Q.**The smallest set A such that A∪{1, 2}={1, 2, 3, 5, 9} is

- {2, 3, 5}
- {3, 5, 9}
- {1, 2, 5, 9}
- {1, 2, }

**Q.**Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let R1 be a relation in X given by R1 = {(x, y) : x – y is divisible by 3} and R2 be another relation on X given by R2 = {(x, y): {x, y} ⊂ {1, 4, 7}} or {x, y} ⊂ {2, 5, 8} or {x, y} ⊂ {3, 6, 9}}. Show that R1 = R2.

**Q.**

Prove that A-(BnC)=(A-B)U (A-C)

**Q.**

Using properties of sets, show that for any two sets A and B, (A∪B)∩(A∩B′)=A.

**Q.**If A={2, 3, 4, 8, 10}, B={3, 4, 5, 10, 12}, C={4, 5, 6, 12, 14}, then (A∪B)∩(A∪C) is

- {2, 3, 4, 5, 8, 10, 12}
- {2, 4, 8, 10, 12}
- {3, 8, 10, 12}
- {2, 8, 10, }

**Q.**

In a class $18$ students took Physics, $23$ students took Chemistry and $24$ students took Mathematics of those $13$ took both Chemistry and Mathematics, $12$ took both Physics and Chemistry and $11$ took both Physics and Mathematics. If $6$ students offered all the three subjects, find out how many took exactly one of the three subjects.

**Q.**

If the sum of three consecutive terms of an A.P is $51$ and the product of last and first term is $273$, then the numbers

$21,17,13$

$20,16,12$

$22,18,14$

$24,20,16$

**Q.**If A is the set of the divisors of 15, B is the set of prime numbers less than 10 and C is the set of even numbers smaller than 9, then (A∪C)∩B is the set

- {1, 3, 5}
- {1, 2, 3}
- {2, 3, 5}
- {2, 5}

**Q.**

In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach physics and mathematics. How many teach physics ?

**Q.**Let A={x:x is a prime factor of 240} and B={y:y is the sum of any two prime factors of 240}. Then which of the following options is true?

- 5∉A∩B
- 7∈A∩B
- 8∈A∩B
- 8∈A∪B

**Q.**

For any two sets A and B, show that the following statements are equivalent :

(i) A⊂B (ii) A−B=ϕ

(iii) A∪B=B (iv) A∩B=A.

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

**Q.**

Which number should be added to the numbers $13,15,19$ so that the resulting numbers be the consecutive terms of an H.P.?

$7$

$6$

$-6$

$-7$

**Q.**In a class of 80 students numbered 1 to 80, all odd numbered students opt for cricket, students whose numbers are divisible by 5 opt for football and students whose numbers are divisible by 7 opt for hockey. The number of students who do not opt any of the three games, is -

- 13
- 24
- 28
- 52

**Q.**The area enclosed by the ellipse x29+y24=1 is

- 3π
- π
- 6π
- 9π

**Q.**

In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many like both coffee and tea ?

**Q.**

Which of the following is/are true?

1. If $A$ is a subset of the universal set $U$, then its complement $A$ is also a subset of $U$.

2. If $U=\left\{1,2,3,\dots ..,10\right\}$ and $A=\left\{1,3,5,7,9\right\}$, then $(A)=A$.

Only I is true

Only II is true

Both I and II are true

None of these

**Q.**Mark the correct alternative in the following question:

If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is

(a)

^{10}C

_{7}(b)

^{10}C

_{7}$\times $ 7! (c) 7

^{10}(d)10

^{7}

**Q.**

Classify True or False:

The absolute value of an integer is always greater than the integer.

- True
- False

**Q.**

If A and B are two sets such that n(A∪B) = 50, n(A) = 28 and n(B) = 32, find n(A∩B).

**Q.**

If

(A) 0 (B)

(C) not defined (D) 1

**Q.**

In the matrix, write:

(i) The order of the matrix (ii) The number of elements,

(iii) Write
the elements *a*_{13},
*a*_{21},
*a*_{33},
*a*_{24},
*a*_{23}

**Q.**Draw a venn diagram of A∪B