Relations Test 40

Result

Relations Test 40

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Weekly Quiz Competition

Question 1
1 / -0

The total number of equivalence relations defined in the set $$S={a,b,c}$$ is

A
$$5$$

B
$$3!$$

C
$$2^{3}$$

D
$$3^{3}$$

E
$$3^{2}$$
Question 2
1 / -0

The relation $$\bot $$ is

A
Reflective

B
Symmetric

C
Transitive

D
Equivalence

Solution
Question 3
1 / -0

The minimum number of elements that must be added to the relation $$R=\{(1, 2), (2, 3)\}$$ on the set $$\{1, 2, 3\}$$ so that it is an equivalence relation.

A
$$3$$

B
$$4$$

C
$$7$$

D
$$6$$

Solution
Question 4
1 / -0

A relation $$R_1$$ is defined set $$A={1,2,3}$$ such that $$R_1\equiv {(1,1),(2,2),(2,3),(3,2)}$$, then minimum number of elements required in $$R_1$$ so that $$R_1$$ becomes R which in an equivalence relation is

A
$$5$$

B
$$3$$

C
$$1$$

D
$$0$$
Question 5
1 / -0

$$R={(1, 2), (2,3),(3 4)}$$ be a relation on the set of natural numbers. Then the last number of elements that must be included inn R to get a new relation S where S is an equivalence relation, is

A
5

B
7

C
9

D
11

Solution

$$ \begin{array}{l} \text { solution: } R=(1,2),(2,3),(3,4) \\ \text { To make it an equivalence relation, we need } \\ \text { to make it Reflexive, symmetric and transitive } \\ \text { at the same time. } \\ \text { Elements needed to make it Reflexive are } \\ (1,1),(2,2),(3,3),(4,4) \end{array} $$
$$ \begin{array}{l} \text { Elements related to make it symmetric are } \\ (2,1),(3,2),(4,3) \\ \text { Elements needed to make it transitive are } \\ (1,3) \text { , }(2,4) \\ \text { so total number of terms required are } 9 \\ \text { Answer: option (c) } \end{array} $$
Question 6
1 / -0

If $$\int\dfrac{2\cos x-\sin x+\lambda}{\cos x-\sin x-2}dx=A In\left|\cos x+\sin x-2\right|+Bx+C$$. Then the ordered triplet $$\left(A,B,\lambda\right)$$, is

A
$$\left(\dfrac{1}{2},\dfrac{3}{2},-1\right)$$

B
$$\left(\dfrac{3}{2},\dfrac{1}{2},-1\right)$$

C
$$\left(\dfrac{1}{2},-1, \dfrac{3}{2}\right)$$

D
$$\left(\dfrac{3}{2},-1, \dfrac{1}{2}\right)$$
Question 7
1 / -0

The maximum number of equivalence relation on the set $$A=\{1,2,3,4\}$$ are

A
$$15$$

B
$$13$$

C
$$20$$

D
$$5$$

Solution
Question 8
1 / -0

The number of reflexive relations of a set with three elements is equal to

A
$$2^{12}$$

B
$$2^9$$

C
$$2^6$$

D
$$2^3$$

Solution
Question 9
1 / -0

Let R be a relation over set N$$\times N$$defined by (a,b)R (c,d) if a + d = b + c then R is ...... ( Here N is the set of all natural numbers)

A
Reflexive only

B
Symmetric only

C
Transitive only

D
Equivalence relation

Solution
Question 10
1 / -0

Let $$s = \{(x, y)| \sin y = \sin x; x, y \in R \}$$, then $$s$$ is

A
Not transitive

B
equivalence

C
transitive but not reflexive

D
partial order relation

Solution