let r 13 4 2 2 4 2 3 3 1 be a relation on the set a 1 2 3 4

Let $$R$$ = {(1,3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set $$A$$ = {1, 2, 3, 4}. The relation $$R$$ is

A. reflexive

B. transitive

C. not symmetric

D. a function

Answer : not symmetric

Solution :
$$\because \,\,\left( {1,1} \right) \notin R$$
⇒ $$R$$ is not reflexive (2, 3) $$ \notin R$$ but (3, 2) $$ \notin R$$
∴ $$R$$ is not symmetric

Releted MCQ Question on
Calculus >> Sets and Relations

Releted Question 1

If $$X$$ and $$Y$$ are two sets, then $$X \cap {\left( {X \cup Y} \right)^c}$$ equals.

A. $$X$$

B. $$Y$$

C. $$\phi $$

D. None of these

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Releted Question 2

The expression $$\frac{{12}}{{3 + \sqrt 5 + 2\sqrt 2 }}$$ is equal to

A. $$1 - \sqrt 5 + \sqrt 2 + \sqrt {10} $$

B. $$1 + \sqrt 5 + \sqrt 2 - \sqrt {10} $$

C. $$1 + \sqrt 5 - \sqrt 2 + \sqrt {10} $$

D. $$1 - \sqrt 5 - \sqrt 2 + \sqrt {10} $$

View Answer

Releted Question 3

If $${x_1},{x_2},.....,{x_n}$$ are any real numbers and $$n$$ is any positive integer, then

A. $$n\sum\limits_{i = 1}^n {{x_i}^2 < {{\left( {\sum\limits_{i = 1}^n {{x_i}} } \right)}^2}} $$

B. $$\sum\limits_{i = 1}^n {{x_i}^2 \geqslant {{\left( {\sum\limits_{i = 1}^n {{x_i}} } \right)}^2}} $$

C. $$\sum\limits_{i = 1}^n {{x_i}^2 \geqslant n{{\left( {\sum\limits_{i = 1}^n {{x_i}} } \right)}^2}} $$

D. none of these

View Answer

Releted Question 4

Let $$S$$ = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of $$S$$ is equal to

A. 25

B. 34

C. 42

D. 41

View Answer

Let $$R$$ = {(1,3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set $$A$$ = {1, 2, 3, 4}. The relation $$R$$ is

Releted MCQ Question on
Calculus >> Sets and Relations

If $$X$$ and $$Y$$ are two sets, then $$X \cap {\left( {X \cup Y} \right)^c}$$ equals.

The expression $$\frac{{12}}{{3 + \sqrt 5 + 2\sqrt 2 }}$$ is equal to

If $${x_1},{x_2},.....,{x_n}$$ are any real numbers and $$n$$ is any positive integer, then

Let $$S$$ = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of $$S$$ is equal to

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Sets and Relations

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Let $$R$$ = {(1,3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set $$A$$ = {1, 2, 3, 4}. The relation $$R$$ is

Releted MCQ Question on Calculus >> Sets and Relations

If $$X$$ and $$Y$$ are two sets, then $$X \cap {\left( {X \cup Y} \right)^c}$$ equals.

The expression $$\frac{{12}}{{3 + \sqrt 5 + 2\sqrt 2 }}$$ is equal to

If $${x_1},{x_2},.....,{x_n}$$ are any real numbers and $$n$$ is any positive integer, then

Let $$S$$ = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of $$S$$ is equal to

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