Sets, Relations and Functions Test

Result

Sets, Relations and Functions Test - 61

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Weekly Quiz Competition

Question 1
4 / -1

Let R be the set of real numbers Statement I A = {(x, y) ϵ R × R : y – x is an integer} is an equivalence relation on R. Statement 2 B = {(x, y) ϵ R × R : x = ay for some rational number α } is an equivalence relation on R.

A
statement 1 is true, Statement 2 is true; statement 2 is correct explanation for statement 1

B
Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1

C
Statement 1 is true, Statement 2 is false

D
Statement 1 is false, Statement 2 is true

Solution
Question 2
4 / -1

Two finite sets have m and n elements. The total number of subsets of the first is 56 more than the total number of subsets of the second set. The values of m and n are

A
7, 6

B
6, 3

C
5, 1

D
8, 7

Solution
Question 3
4 / -1

A
15

B
3

C
45

D
None of these

Solution
Question 4
4 / -1

Let R be the real line. Consider the following subsets of the plane R × R
S = {(x, y) : y = x + 1 and 0 < x < 2}
T = {(x, y) : x – y is an integer}
Which one of the following is true ?

A
Both S and T are equivalence relation on R

B
S is an equivalence relation on R but T is not

C
T is an equivalence relation on R but S is not

D
Neither S nor T is an equivalence relation on R

Solution
Question 5
4 / -1

If A = [x : f(x) = 0] and B = [x : g(x) = 0], then A ∩ B will be

A

B

C

D
None of these

Solution
Question 6
4 / -1

In a certain town 25% families own a phone and 15% own a car, 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard
1. 10% families own both a car and a phone
2. 35% families own either car or a phone
3. 40,000 families live in the town ?
Which of the above statements are correct?

A
1 and 2

B
1 and 3

C
2 and 3

D
1,2 and 3

Solution
Question 7
4 / -1

Let A = {2,4,6,8}. A relation R on A is defined by R = {(2,4), (4, 2),(4, 6), (6, 4)}. Then R is

A
Anti – symmetric

B
Reflexive

C
Symmetric

D
Transitive
Question 8
4 / -1

Let N denote the set of all natural numbers and R be the relation on N × N defined by (a, b) R (c, d) if ad(b + c) = bc(a + d), then R is

A
Symmetric only

B
Reflexive only

C
Transitive only

D
An equivalence relation
Question 9
4 / -1

The solution set of 8x = 6 (mod 14), x ϵ Z, are

A
[8] ∪ [6]

B
[8] ∪ [14]

C
[6] ∪ [13]

D
[8] ∪ [6] ∪ [13]

Solution
Question 10
4 / -1

If A = {1,2,3}, B = {1,4,6,9} and R is a relation from A to B defined by ‘x’ is greater than ‘y’. The range of R is

A
{1,4,6,9}

B
{4,6,9}

C
{1}

D
None of these