Relations Test 43

Result

Relations Test 43

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Question 1
1 / -0

Let $$R_1$$ be a relation defined by
$$R_1 =$${ $$(a, b)| a >b , a, b \epsilon R$$}. Then $$R_1$$ is

A
an equivalence relation on R

B
reflexive, transitive but not symmetric

C
symmetric, transitive but nor reflective

D
neither transitive nor reflective but symmetric
Question 2
1 / -0

If a relation { R } on the set { 1,2,3 } be definedby R = { ( 1,2 ) } then { R } is

A
reflexive

B
transitive

C
Symmetric

D
None of these

Solution
Question 3
1 / -0

The relation R defined in N as $$aRb \Leftrightarrow b$$ is divisible by a is

A
Reflexive but not symmetric

B
Symmetric but not transitive

C
Symmetric and transitive

D
Equivalence relation
Question 4
1 / -0

If $$(x^{2}-2)+(y+3)i=7+4i$$ then x and y are

A
$$\pm 3 and 4 $$

B
$$\pm \sqrt{5} and 4 $$

C
$$\pm 3 and 1 $$

D
None of these

Solution
Question 5
1 / -0

Let $$R = \left \{(2, 3), (3, 3), (2, 2), (5, 5), (2, 4), (4, 4), (4, 3)\right \}$$ be a relation on the set $$\left \{2, 3, 4, 5\right \}$$, then

A
$$R$$ is reflexive and symmetric but not transitive

B
$$R$$ is reflexive and transitive but not symmetric

C
$$R$$ is symmetric and transitive but not reflexive

D
$$R$$ is an equivalence relation

Solution
Question 6
1 / -0

If $$g(f(x))= |sinx|$$ and $$g(f(x))= sin^2 \sqrt{x},$$ then

A
$$f(x)= \sqrt{x}, \ g(x)= sin^2x$$

B
$$f(x) = sin \sqrt{x}, \ g(x)= x^2$$

C
$$f(x)= \sqrt{sinx}, \ g(x)= x^2$$

D
$$f(x)= |x|, \ g(x)= sin^2 x$$

Solution
Question 7
1 / -0

If $$A = \left \{1, 2, 3, 4, 5\right \}$$ then

A
The number of relation on $$A$$ is $$2^{25}$$

B
The number of relation on $$A$$ is $$2^{20}$$

C
The number of reflexive relation on $$A$$ is $$20^{20}$$

D
The number of reflexive relation on $$A$$ is $$2^{15}$$

Solution
Question 8
1 / -0

If $$A=\left\{1,2,4 \right\}$$, $$B=\left\{1,4,6,9 \right\}$$ and $$R$$ is a relation from $$A$$ to $$B$$ defined by $$x$$ is greater than $$y$$. The rangle of $$R$$ is :

A
$$\left\{1,4,6,9 \right\} $$

B
$$\left\{4,6,9 \right\} $$

C
$$\left\{ 1 \right\} $$

D
none of these

Solution
Question 9
1 / -0

If $$A=\{ 1,2,3\} $$ then the number of equivalance relation containing the element {1,2} is :

A
1

B
2

C
3

D
14
Question 10
1 / -0

Let S be the set of all straight lines in a plane. Let R be a relation on S defined by $$a$$ R $$b\Leftrightarrow a||b$$. Then, R is?

A
Reflexive and symmetric but not transitive

B
Reflexive and transitive but not symmetric

C
Symmetric and transitive but not reflexive

D
An equivalence relation

Solution