CBSE Questions for Class 11 Commerce Applied Mathematics Relations Quiz 3 - MCQExams.com

Let $$R$$ be a relation such that $$R = \{(1,4), (3, 7), (4, 5), (4, 6), (7, 6) \}$$ then $$(R^{-1} oR)^{-1} =$$
  • $$\{(1, 1), (3, 3), (4, 4), (7, 7), (4, 7), (7, 4), (4, 3)\}$$
  • $$\{(1, 1), (3, 3), (4, 4), (7, 7), (4, 7), (7, 4) \}$$
  • $$\{(1, 1), (3, 3), (4, 4) \}$$
  • $$\phi$$
If $$A$$ and $$B$$ are two sets, then $$A \times B  = B \times A$$ if
  • $$A \subset B$$
  • $$B \subset A$$
  • $$A = B$$
  • None of these
Let $$R$$ be the relation on $$Z$$ defined by $$R = \{(a, b): a, b \in z, a - b$$ is an integer$$\}$$. Find the domain and Range of $$R$$.
  • $$z, z$$
  • $$z^+, z$$
  • $$z, z^-$$
  • None of these
Let $$R$$ be a relation on the set $$N$$ given by $$R=\left\{ \left( a,b \right) :a=b-2,b>6 \right\}$$. Then
  • $$(2,4)\in R$$
  • $$(3,8)\in R$$
  • $$(6,8)\in R$$
  • $$(8,7)\in R$$
Which of the following is not an equivalence relation on $$Z$$?
  • $$aRb\Leftrightarrow a+b$$ is an even integer
  • $$aRb\Leftrightarrow a-b$$ is an even integer
  • $$aRb\Leftrightarrow a< b$$
  • $$aRb\Leftrightarrow a= b$$
A relation $$R$$ is defined from $$\left\{ 2,3,4,5 \right\} $$ to $$\left\{ 3,6,7,10 \right\} $$ by:
$$xRy\Leftrightarrow x$$ is relatively prime to $$y$$. Then, domain of $$R$$ is
  • $$\left\{ 2,3,5 \right\} $$
  • $$\left\{ 3,5 \right\} $$
  • $$\left\{ 2,3,4 \right\} $$
  • $$\left\{ 2,3,4,5 \right\} $$
The relation $$R$$ in $$N\times N$$ such that $$(a,b)R(c,d)\Leftrightarrow a+d=b+c$$ is
  • reflexive but not symmetric
  • reflexive and transitive but not symmetric
  • an equivalence relation
  • none of these
Let $$R$$ be the relation over the set of all straight lines in a plane such that $${l}_{1}$$ $$R$$ $${l}_{2}\Leftrightarrow {l}_{1}\bot {l}_{2}$$. Then, $$R$$ is
  • symmetric
  • reflexive
  • transitive
  • an equivalence relation
If $$A=\left\{ a,b,c \right\} $$, then the relation $$R=\left\{ \left( b,c \right)  \right\} $$ on $$A$$ is
  • reflexive only
  • symmetric only
  • transitive only
  • reflexive and transitive only
Let $$A=\left\{ 1,2,3 \right\} $$. Then, the number of equivalence relations containing $$(1,2)$$ over set A is
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
Let $$A=\left\{ 1,2,3 \right\} $$ and $$R=\left\{ \left( 1,2 \right) ,\left( 2,3 \right) ,\left( 1,3 \right)  \right\} $$ be a relation on $$A$$. Then $$R$$ is
  • neither reflexive nor transitive
  • neither symmetric nor transitive
  • transitive
  • none of these
If $$A=\left\{ 1,2,3 \right\} , B=\left\{ 1,4,6,9 \right\} $$ and $$R$$ is a relation from $$A$$ to $$B$$ defined by $$x$$ is greater than $$y$$. The range of $$R$$ is
  • $$\left\{ 1,4,6,9 \right\} $$
  • $$\left\{ 4,6,9 \right\} $$
  • $$\left\{ 1 \right\} $$
  • none of these
A relation $$\phi$$ from $$C$$ to $$R$$ is defined by $$x\phi y\Leftrightarrow \left| x \right| =y$$. Which one is correct?
  • $$(2+3i)\phi 13$$
  • $$3\phi (-3)$$
  • $$(1+i)\phi 2$$
  • $$i\phi 1$$
Let $$R$$ be a relation on $$N$$ defined by $$x+2y=8$$. The domain of $$R$$ is
  • $$\left\{ 2,4,8 \right\} $$
  • $$\left\{ 2,4,6,8 \right\} $$
  • $$\left\{ 2,4,6 \right\} $$
  • $$\left\{ 1,2,3,4 \right\} $$
If $$A=\left\{ 1,2,3 \right\} $$, then a relation $$R=\left\{ \left( 2,3 \right)  \right\} $$ on $$A$$ is
  • symmetric and transitive only
  • symmetric only
  • transitive only
  • none of these
Let $$A=\left\{ 1,2,3 \right\} $$ and consider the relation $$R=\left\{ \left( 1,1 \right) ,\left( 2,2 \right) \left( 3,3 \right) ,\left( 1,2 \right) ,\left( 2,3 \right) ,\left( 1,3 \right)  \right\} $$, then $$R$$ is
  • reflexive but not symmetric
  • reflexive but not transitive
  • symmetric and transitive
  • neither symmetric nor transitive
If $$n(A) = 4$$ and $$n(B) = 5$$, then $$n(A \times  B) = $$
  • $$20$$
  • $$25$$
  • $$4$$
  • $$15$$
In the set $$Z$$ of all integers, which of the following relation $$R$$ is an equivalence relation?
  • $$xRy:$$ if $$x\le y$$
  • $$xRy:$$ if $$x-= y$$
  • $$xRy:$$ if $$x- y$$ is an even integer
  • $$xRy:$$ if $$x\equiv y$$ (mod 3)
Let $$L$$ denote the set of all straight lines in a plane, Let a relation $$R$$ be defined by $$lRm$$, iff $$l$$ is perpendicular to $$m$$ for all $$l \in L$$. Then, $$R$$ is
  • reflexive
  • symmetric
  • transitive
  • none of these
Let $$T$$ be the set of all triangles in the Euclidean plane, and let a relation $$R$$ on $$T$$ be defined as $$aRb$$, if $$a$$ is congruent to $$b$$ for all $$a,b\in T$$. Then, $$R$$ is
  • reflexive but not symmetric
  • transitive but not symmetric
  • equivalence
  • none of these
Let $$R$$ be a relation on the set $$N$$ of natural numbers defined by $$nRm$$, iff $$n$$ divides $$m$$. Then, $$R$$ is
  • Reflexive and symmetric
  • Transitive and symmetric
  • Equivalence
  • Reflexive, transitive but not symmetric
The relation $$R=\left\{ \left( 1,1 \right) ,\left( 2,2 \right) \left( 3,3 \right)  \right\} $$ on the set $$A=\left\{ 1,2,3 \right\} $$ is
  • symmetric only
  • reflexive only
  • an equivalence relation
  • transitive only
Which one of the following relations on Z is equivalence relation?
  • $$xR_1 y\Leftrightarrow |x| = |y|$$
  • $$xR_2 y\Leftrightarrow x \geq y$$
  • $$xR_3 y\Leftrightarrow \dfrac{x}{y}$$
  • $$xR_4 y\Leftrightarrow x < y$$
Let $$R$$ be a reflexive relation on a finite set $$A$$ having $$n$$ elements, and let there be $$m$$ ordered pairs in $$R,$$ then:
  • $$m\geq n$$
  • $$m\leq n$$
  • $$m=n$$
  • $$m< n$$
Total number of equivalence relations defined in the set $$S =\{a,b,c\}$$ is
  • $$5$$
  • $$3$$!
  • $$2^{3}$$
  • $$3^{3}$$
If relation $$R$$ is defined by $$\mathrm{R}=\{(\mathrm{x},\ \mathrm{y}):2\mathrm{x}^{2}+3\mathrm{y}^{2}\leq 6\}$$, then the domain of $$\mathrm{R}$$ is
  • $$[-3,3]$$
  • $$[-\sqrt{3},\sqrt{3}]$$
  • $$[-\sqrt{2},\sqrt{2}]$$
  • $$[-2,2]$$
If $$\displaystyle A=\left \{ 2, 3, 5 \right \}, B=\left \{ 2, 5, 6 \right \}$$ then  $$\left ( A-B \right )\times \left ( A\cap B \right )$$ is
  • $$\displaystyle \left \{ \left ( 3, 2 \right ), \left ( 3, 3 \right ), \left ( 3, 5 \right )\right \}$$
  • $$\displaystyle \left \{ \left ( 3, 2 \right ), \left ( 3, 5 \right ), \left ( 3, 6 \right )\right \}$$
  • $$\displaystyle \left \{ \left ( 3, 2 \right ), \left ( 3, 5 \right )\right \}$$
  • None of these
The domain and range of relation $$R=\{(x,y) | x, y \in N$$, $$x+2y=5\} $$ is?
  • $$\{1,3\}, \{2,1\}$$
  • $$\{2,1\}, \{3,2\}$$
  • $$\{1,3\}, \{1,1\}$$
  • $$\{1,2\}, \{1,3\}$$
Let $$A$$ be a non-empty set such that $$A \times A$$ has $$9 $$ elements among which are found $$(-1, 0)$$ and $$(0, 1)$$, then
  • $$A=\left\{ -1,0 \right\}$$
  • $$A=\left\{ 0,1 \right\}$$
  • $$A=\left\{ -1,0,1 \right\}$$
  • $$A=\left\{ -1,1 \right\}$$
Given the relation $$R =\{(1,2) (2,3)\}$$ on the set $$A=\{1,2,3\}$$, the minimum number of ordered pairs which when added to $$R$$ to make it an equivalence relation is
  • $$5$$
  • $$6$$
  • $$7$$
  • $$8$$
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