Sets and Relations · Mathematics · WB JEE

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 of the following statement is then true?

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

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 value of (fog)($$-$$1) is

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 function f is

The function $$f(x) = \sec \left[ {\log \left( {x + \sqrt {1 + {x^2}} } \right)} \right]$$ is

The number of reflexive relations on a set $A$ of $n$ elements is equal to

In R, a relation p is defined as follows: $$\forall a, b \in \mathbb{R}, a p$$ holds iff $$a^2-4 a b+3 b^2=0$$. Then

Let A be the set of even natural numbers that are < 8 & B be the set of prime integers that are $$<7$$ The number of relations from A to B are

For the real numbers $$x$$ & $$y$$, we write $$x$$ p y iff $$x-y+\sqrt{2}$$ is an irrational number. Then relation p 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 mapping. Then

For the mapping $$f:R - \{ 1\} \to R - \{ 2\} $$, given by $$f(x) = {{2x} \over {x - 1}}$$, which of the following is correct?

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