CBSE Questions for Class 11 Commerce Applied Mathematics Relations Quiz 14 - MCQExams.com

If n | m means that n is a factor of m, the relation | is
  • reflexive and symmetric
  • transitive and symmetric
  • reflexive, transitive and symmetric
  • reflexive, transitive and not symmetric
Let N denote the set of all natural numbers and R a relation on N $$\times$$ N. Which of the following is an equivalence relation?
  • (a, b, c) R (c, d) if ad (b + c) = bc (a +d)
  • (a, b) R (c, d) if a + d = b + c
  • (a, b) R (c, d) if ad = bc
  • (a, d) R (b, c) if a - d = b - c
The relation R {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A {1, 2, 3} is
  • reflexive but not symmetric
  • reflexive but not transitive
  • symmetric and transitive
  • neither symmetric nor transitive
The relation "is subset of" on the power set P(A) of a set A is
  • symmetric
  • anti-symmetric
  • equivalence relation
  • reflexive
The minimum number of elements that must be added to the relation R {(1, 2), (2, )} on the set of natural numbers so that it is an equivalence is
  • 4
  • 7
  • 6
  • 5
Let X be a non-empty set and P(X) be the set of all subsets of X. For A, B $$\subset$$ P(X), ARB if and only if $$A \cap B = \phi$$ then the relation
  • R is not reflexive
  • R is symmetric
  • R is not transitive
  • R is an equivalence relation
Let $$R_1$$ and $$R_2$$ be equivalence relations on a set A, then $$R_1 \cup R_2$$ may or may not be
  • reflexive
  • symmetric
  • transitive
  • anti-symmetric
Let N denote the set of all natural numbers and R a relation on N $$\times$$ N. Which of the following is an equivalence relation?
  • (a, b) R (c, d) if ad (b + c) = bc (a + d)
  • (a, b) R (c, d) if a + d = b + c
  • (a, b) R (c, d) if ad = bc
  • all the given
Let A and B be finite sets containing m and n elements respectively. The number of relations that can be defined from A to B is
  • $$mn$$
  • $$2^{mn}$$
  • $$2^{m+n}$$
  • $$n^m$$
Let A = {1, 2, 3}. Which of the following is not an equivalence relation on A?
  • {(1, 1), (2, 2), (3, 3)}
  • {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}
  • {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}
  • {(1, 1) (2, 1)}
Range of the function $$f(x)=\dfrac{sec^2\,x-tanx}{sec^2\,x+tanx}-\dfrac{\pi}{2}<x<\dfrac{\pi}{2}$$, is 
  • R
  • $$R-(\dfrac{1}{3},3)$$
  • $$[\dfrac{1}{3},3]$$
  • $$[-1,\dfrac{5}{3}]$$
In the set of all $$3\times 3$$ real matrices a relation is defined as follows. A matrix A is related to a matrix B if and only if there is a non-singular $$3\times 3$$ matrix P such that $$B=P^{-1}AP$$. This relation is 
  • Reflexive, Symmetric but not Transitive
  • Reflexive, Transitive but not Symmetric
  • Symmetric, Transitive but not Reflexive
  • An Equivalence relation
Let $$R = \left \{(2, 3), (3, 4)\right \}$$ be a relation defines on the set of natural numbers. The minimum number of ordered pairs required to be added in $$R$$ so that enlarged relation be comes an equivalence relation is
  • $$3$$
  • $$5$$
  • $$7$$
  • $$9$$
If $$A$$ and $$B$$ have $$n$$ elements in common, then the number of elements common to $$A\times B$$ and $$B\times A$$ is
  • $$n$$
  • $$2n$$
  • $$n^2$$
  • $$0$$
Let $$R$$ and $$S$$ be two non-void relations on a set $$A$$. Which of the following statements is false?
  • $$R$$ and $$S$$ are transitive implies $$R\cap S$$ is transitive
  • $$R$$ and $$S$$ are transitive implies $$R\cup S$$ is transitive
  • $$R$$ and $$S$$ are symmetric imples $$R\cup S$$ is symmetric
  • $$R$$ and $$S$$ reflexive implies $$R\cap S$$
Number of ordered triplets $$(p,q,r)$$ where $$1\le p,q,r\le 10 $$ such that $${ 2 }^{ p }+{ 3 }^{ q }+{ 5 }^{ r }$$ is a multiple of $$4\left( p,q,e\in N \right) $$
  • $$1000$$
  • $$500$$
  • $$250$$
  • $$125$$
We define a binary relation $$\sim $$ on the set of all $$3\times 3$$ matrices as $$A\sim  B$$ if and only if there exist invertible matrices $$P$$ and $$Q$$ such that $$B=PA{Q}^{-1}$$. The binary relation $$\sim $$ is
  • Neither reflexive nor symmetric
  • Reflexive and symmetric but not transitive
  • Symmetric and transitive but not reflexive
  • An equivalence relation
Let $$R$$ a relation on the set $$N$$ be defined by $$\left\{ \left( x,y \right) |x,y\in N,2x+y=41 \right\}$$. Then $$R$$ is 
  • Reflexive
  • Symmetric
  • Transitive
  • None of these
If R is a reflexive relation defined on a finite set A and $$n(A)=p$$, and $$n(R)=q$$, then?
  • $$p=q$$
  • $$p\leq q$$
  • $$p\geq q$$
  • None of these
Let R be a relation on the set of integers given by $$ aRb \leftrightarrow a = 2^k .b $$ for some integer $$k.$$ Then $$R$$ is 
  • an equivalence relation
  • reflexive and transitive but not symmetric
  • reflexive and transitive but not transitive
  • symmetric and transitive but nor reflexive
Total number of equivalence relations defined in the set $$S=\left\{a, b, c\right\}$$ is?
  • $$5$$
  • $$3!$$
  • $$2^3$$
  • $$3^3$$
Let $$A={1,2,3}$$. Then number of equivalence relations containing $$(1,2)$$ is
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
If R is a reflexive relation on a finite set A having n-elements, and there are m ordered pairs in R. then?
  • $$m \geq n$$
  • $$m\leq n$$
  • $$m = n$$
  • $$m\neq n$$
Let R be a relation from $$ A=\{1,2,3,4\}$$ to $$B=\{1,3,5\}$$such that R=[(a,b):a<b where a\in{A} and b\in{B}].What is $$RoR^{-1} $$ equal to
  • $$(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)$$
  • $$(3,1),(5,1),(3,2)(5,2),(5,3),(5,4)$$
  • $$(3,3),(3,5),(5,3),(5,5)$$
  • $$(3,3),(3,4),(4,5)$$
$$f:\left( { - \infty ,\infty } \right) \to \left( {0,1} \right]$$ defined by $$f\left( x \right) = \frac{1}{{{x^2} + 1}}$$ is 
  • one -one but not onto
  • onto but not one-one
  • bijective
  • neither one-one nor onto
Let $$X=\left\{ x \epsilon {R};\cos(\sin\ x)=\sin(\cos\ x)\right\}$$. The number of elements in $$X$$ is 
  • $$0$$
  • $$2$$
  • $$4$$
  • $$ not\ finite$$
If the relation $$R:A \to B$$ where $$A = \left\{ {1,2,3,4} \right\},B = \left\{ {1,3,5} \right\}$$ is defined by $$R = \left\{ {\left( {x,y} \right):x < y,x \in A,y \in B} \right\}$$ then $$Ro{R^{ - 1}} = $$ 
  • $$\left\{ {\left( {1,3} \right),\left( {1,5} \right),\left( {2,3} \right),\left( {2,5} \right),\left( {3,5} \right),\left( {4,5} \right)} \right\}$$
  • $$\left\{ {\left( {3,1} \right),\left( {5,1} \right),\left( {3,2} \right),\left( {5,2} \right),\left( {5,3} \right),\left( {5,4} \right)} \right\}$$
  • $$\left\{ {\left( {3,3} \right),\left( {3,5} \right),\left( {5,3} \right),\left( {5,5} \right)} \right\}$$
  • $$\left\{ {\left( {3,3} \right).\left( {3,4} \right),\left( {4,5} \right)} \right\}$$
For real number $$x$$ and $$y$$, define a relationship $$R$$ {;$$x\ Ry$$ if and only if $$x-y+\sqrt{2}$$ is an irrational number }. Then the relation $$R$$ is
  • Reflexive
  • symmetric
  • transitive
  • an equivalence relation
Let $$X$$ be a family of sets and $$R$$ be a relation on $$X$$ defined by $$'A$$ is disjoint from $$B ^ { \prime }$$ . Then $$R$$ is _________.
  • Reflexive
  • Symmetric
  • Anti-symmetric
  • Transitive
$$p \Rightarrow \,q$$ can also be written as 
  • $$p \Rightarrow \, \sim q$$
  • $$ \sim p \vee q$$
  • $$ \sim q \Rightarrow \, \sim p$$
  • None of these
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