Let P = ( x,y ):| x^2 + y^2 | = 1,x,y R . Then P is :

let p xy x 2 y 2 1xy in r then p is 640026785

Let $$P = \left\{ {\left( {x,\,y} \right):\left| {{x^2} + {y^2}} \right| = 1,\,x,\,y\, \in \,R\,} \right\}.$$ Then $$P$$ is :

A. Reflexive

B. Symmetric

C. Transitive

D. Anti-symmetric

Answer : Symmetric

Solution :
Obviously, the relation is not reflexive and transitive but it is symmetric, because $${x^2} + {y^2} = 1\,\, \Rightarrow {y^2} + {x^2} = 1$$

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

View Answer

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 $$P = \left\{ {\left( {x,\,y} \right):\left| {{x^2} + {y^2}} \right| = 1,\,x,\,y\, \in \,R\,} \right\}.$$ Then $$P$$ 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

Practice More MCQ Question on Maths Section

Let $$P = \left\{ {\left( {x,\,y} \right):\left| {{x^2} + {y^2}} \right| = 1,\,x,\,y\, \in \,R\,} \right\}.$$ Then $$P$$ 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

Practice More Releted MCQ Question on Sets and Relations

Practice More MCQ Question on Maths Section

Releted MCQ Question on
Calculus >> Sets and Relations

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Sets and Relations