List of top Mathematics Questions on sets

Let $P(S)$ denote the power set of $S = \{1, 2, 3, \ldots, 10\}$ . Define the relations $R_1$ and $R_2$ on $P(S)$ as $A R_1 B$ if $(A \cap B^c) \cup (B \cap A^c) = ,$ and $A R_2 B$ if $A \cup B^c = B \cup A^c,$ for all $A, B \in P(S)$ . Then:

Let S = {1, 2, 3, 4, 5, 6}. Then the number of one-one functions

f : S → P(S)

, where

P(S)

denotes the power set of S, such that

f(n) ⊂ f(m)

where

n < m,

is:

If

P = \{3m : m \in \mathbb{N}\}

and

Q = \{3m : m \in \mathbb{N}\}

are two sets, then

Let S = {1, 2, 3, 4, 5}
if f : S → P(S), where P(S) is power set of S. Then number of one-one functions f can be made is

Let S = {1, 2, 3, 4}.Then the number of elements in the set {f : S × S → S : f is onto and f(a,b)=f(b,a) ≥ a ∀ (a, b)∈ S × S is _____.

Let A = {x∈Z: -1 ≤ x < 4} and let B = {x ∈ Z:0 <

\frac{x}{2}

≤ 3}. Then A∩B is equal to

Let $R$ be a relation on the set $\mathbb{N}$ defined by

\{(x, y) \mid x, y \in \mathbb{N}, \, 2x + y = 41\}.

{Then,

R

is:}

The function $f : \mathbb{R} \to \mathbb{R}$ defined by $f(x) = x^2 + x$ is:

A class has 175 students. The following data shows the number of students opting for one or more subjects. Maths = 100, Physics = 70, Chemistry = 40, Maths and Physics = 30, Maths and Chemistry = 28, Physics and Chemistry = 23, Maths, Physics, and Chemistry = 18.
How many have offered Maths alone?

If n(A∪B)=97, n(A∩B) = 23 and n(A-B)=39, then n(B) is equal to