Sets Test

Result

Sets Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and C be the set of points inside a unit circle, then which of the following statements is true?

A
R = {(x, y) : 0 < x < a, 0 < y < b}

B
C = {(x , y) : x² + y² + < 1}

C
R U C = R

D
None of these
Question 2
1 / -0

In a college, 40% of the students play basketball, 34% play tennis and 234 play both the sports. The number of students who play neither basketball nor tennis is 52% of the total students. What is the total number of students in the college?

A
1050

B
1000

C
900

D
None of these
Question 3
1 / -0

In a survey of political preference, people were asked to give their preference on three government proposals I, II and III. 78% were in favour of atleast one of the proposals, 50% favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% favoured all the three proposals, what percent of people favoured more than one of the three proposals?

A
5%

B
12%

C
17%

D
None of these
Question 4
1 / -0

If A is any set , then

A
A∪A′=U

B
A∩A′=U

C
A∩A′=A

D
A∪A′=ϕ

Solution

A∪A′={x∈U:x∈A}∪{x∈U:x∉A}=U
Question 5
1 / -0

Let A = { a,b,c } , B = { b,c,d } , C = { a,b,d,e } , then A∩(B∪C) is

A
{ a,b,d,e }

B
{ a,b,c }

C
{ e }

D
{ b,c,d }

Solution

HereA={a,b,c},B={b,c,d}andC

={a,b,d,e}

B∪C={a,b,c,d,e}

A∩(B∪C)={a,b,c}
Question 6
1 / -0

If A and B are two sets , then A∪B=A∩B iff

A
A = B

B
B ⊆ A

C
A ⊆ B

D
none of these

Solution

LetA=B,Then,

A∪B=AandA∩B=A

⇒A∪B=A∩B

Thus,A=B⇒A∪B=A∩B....(2)

Conversely,letA∪B=A∩B,now we have to prove that A=B.

Letx∈A

⇒x∈A∪B

⇒x∈A∩B

⇒x∈Aandx∈B

⇒x∈Bso,A⊂B.....(2)

Let y∈B

⇒y∈A∪B

⇒y∈A∩B

⇒y∈Aandy∈B

⇒y∈ASo,B⊂A.....(3)

Thus,A∪B=A∩B⇒A=B.....(4)

From(1)and(4),

wegetA∪B=A∩B⇔A=B
Question 7
1 / -0

The power set of {2, 5} is

A
{, {2}, {5}, {2, 5}}

B
{2, 5, {5}}

C
{{2}, {5}, {2, 5}}

D
None of these
Question 8
1 / -0

If A and B be any two sets , then (A∪B)′ is equal to

A
A∪B

B
A∩B

C
A′∪B′

D
A′∩B′

Solution

x∈(A∪B)′

⇒x∉(A∪B)

⇒x∉Aorx∉B

⇒x∈A′andx∈B′

⇒x∈A′∩B′

⇒(A∪B)′⊆A′∩B′

Similarly we can show (A′∩B′)⊆(A∪B)′

so (A∪B)′=(A′∩B′)
Question 9
1 / -0

In a town, 48% people are educated, 51% people are young, 60% are servicemen, 24% are educated and young. There are 25% are young and servicemen, 27% are educated and servicemen and 5% fit in all the three categories. What is the ratio of educated or young, but not servicemen to young or servicemen but not educated?

A
19/20

B
4/5

C
7/10

D
None of these

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Re-Attempt Weekly Quiz Competition

Sets Test - 3

Result

Sets Test - 3

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SHARING IS CARING

Question 1

R = {(x, y) : 0 < x < a, 0 < y < b}

C = {(x , y) : x2 + y2 + < 1}

R U C = R

None of these

Question 2

1050

1000

900

None of these

Question 3

5%

12%

17%

None of these

Question 4

A∪A′=U

A∩A′=U

A∩A′=A

A∪A′=ϕ

Solution

Question 5

{ a,b,d,e }

{ a,b,c }

{ e }

{ b,c,d }

Solution

Question 6

A = B

B ⊆ A

A ⊆ B

none of these

Solution

Question 7

{, {2}, {5}, {2, 5}}

{2, 5, {5}}

{{2}, {5}, {2, 5}}

None of these

Question 8

A∪B

A∩B

A′∪B′

A′∩B′

Solution

Question 9

19/20

4/5

7/10

None of these

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C = {(x , y) : x² + y² + < 1}