Sets and Relations
Previous Years Questions

MCQ (Single Correct Answer)

Three sets A, B, C are such that A = B $$\cap$$ C and B = C $$\cap$$ A, then
A mapping f : N $$\to$$ N where N is the set of natural numbers is defined as f(n) = n2 for n odd f(n) = 2n + 1 for n even for n $$\in$$ N. Then f is...
The mapping f : N $$\to$$ N given by f(n) = 1 + n2, n $$\in$$ N where N is the set of natural numbers, is
A function f : A $$\to$$ B, where A = {x/$$-$$1 $$\le$$ x $$\le$$ 1} and B = {y/1 $$\le$$ y $$\le$$ 2} is defined by the rule y = f(x) = 1 + x2. Which...
Let A = {1, 2, 3} and B = {2, 3, 4}, then which of the following relations is a function from A to B?
For any two sets A and B, A $$-$$ (A $$-$$ B) equals
A mapping from IN to IN is defined as follows: $$f:IN \to IN$$ $$f(n) = {(n + 5)^2},\,n \in IN$$ (IN is the set of natural numbers). Then...
The domain of definition of the function $$f(x) = \sqrt {1 + {{\log }_e}(1 - x)} $$ is
Let R be the set of real numbers and the mapping f : R $$\to$$ R and g : R $$\to$$ R be defined by f(x) = 5 $$-$$ x2 and g(x) = 3x $$-$$ 4, then the v...
If A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5, 6} are two sets, and function f : A $$\to$$ B is defined by f(x) = x + 2 $$\forall$$ x$$\in$$ A, then the fun...
The function $$f(x) = \sec \left[ {\log \left( {x + \sqrt {1 + {x^2}} } \right)} \right]$$ is
The domain of the function $$f(x) = \sqrt {{{\cos }^{ - 1}}\left( {{{1 - |x|} \over 2}} \right)} $$ is
Let A, B, C are subsets of set X. Then consider the validity of the following set theoretic statement:
Let X be a nonvoid set. If $$\rho_1$$ and $$\rho_2$$ be the transitive relations on X, then ($$\circ$$ denotes the composition of relations)...
Let $$\rho$$ be a relation defined on set of natural numbers N, as $$\rho = \{ (x,y) \in N \times N:2x + y = 4\} $$. Then domain A and range B are...
A is a set containing n elements. P and Q are two subsets of A. Then the number of ways of choosing P and Q so that P $$\cap$$ Q = $$\varphi $$ is...
Let S, T, U be three non-void sets and f : S $$\to$$ T, g : T $$\to$$ U and composed mapping g . f : S $$\to$$ U be defined. Let g . f be injective ma...
For the mapping $$f:R - \{ 1\} \to R - \{ 2\} $$, given by $$f(x) = {{2x} \over {x - 1}}$$, which of the following is correct?
Let A, B, C be three non-void subsets of set S. Let (A $$\cap$$ C) $$\cup$$ (B $$\cap$$ C') = $$\phi$$ where C' denote the complement of set C in S. T...
Let R be the real line. Let the relations S and T or R be defined by $$S = \{ (x,y):y = x + 1,0 ...
Let the relation p be defined on R by a p b holds if and only if a $$ - $$ b is zero or irrational, then
Let $$A = \{ x \in R: - 1 \le x \le 1\} $$ and $$f:A \to A$$ be a mapping defined by $$f(x) = x\left| x \right|$$. Then f is
Let p1 and p2 be two equivalence relations defined on a non-void set S. Then
Let the relation $$\rho $$ be defined on R as a$$\rho $$b if 1 + ab > 0. Then,
Let f : X $$ \to $$ Y and A, B are non-void subsets of Y, then (where the symbols have their usual interpretation)
Let S, T, U be three non-void sets and f : S $$ \to $$ T, g : T $$ \to $$ U be so that gof : s $$ \to $$ U is surjective. Then,
On R, a relation $$\rho $$ is defined by x$$\rho $$y if and only if x $$-$$ y is zero or irrational. Then,
On the set R of real numbers, the relation $$\rho $$ is defined by x$$\rho $$y, (x, y) $$ \in $$ R.
Let $$\rho $$ be a relation defined on N, the set of natural numbers, as$$\rho $$ = {(x, y) $$ \in $$ N $$ \times $$ N : 2x + y = 41}. Then
On the set R of real numbers we define xPy if and only if xy $$ \ge $$ 0. Then, the relation P is
On R, the relation $$\rho$$ be defined by 'x$$\rho$$y holds if and only if x $$-$$ y is zero or irrational'. Then,
On set A = {1, 2, 3}, relations R and S are given byR = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)},S = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}. Then,...

MCQ (More than One Correct Answer)

If R and R$$^1$$ are equivalence relations on a set A, then so are the relations
Let R and S be two equivalence relations on a non-void set A. Then
On R, the set of real numbers, a relation $$\rho $$ is defined as 'a$$\rho $$b if and only if 1 + ab > 0'. Then,
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