List of top Mathematics Questions on sets

If $ R $ is the smallest equivalence relation on the set $ \{1, 2, 3, 4\} $ such that $ \{(1,2), (1,3)\} \subseteq R $, then the number of elements in $ R $ is ______.

Number of subsets of set of letters of word 'MONOTONE' is:

In a statistical investigation of 1003 families of Calcutta, it was found that 63 families have neither a radio nor a TV, 794 families have a radio, and 187 have a TV. The number of families having both a radio and a TV is:

If $ a>0, b>0, c>0 $ and $ a, b, c $ are distinct, then $ (a + b)(b + c)(c + a) $ is greater than:

The modulus of the complex number $ z $ such that $ |z + 3 - i| = 1 $ and $ \arg(z) = \pi $ is equal to:

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:

The number of elements in the set $\{n ∈ Z : n^2-10n+19| < 6\}$ is __.

If the set $\left( Re \left( \frac{z-\bar{z}+z\bar{z}}{2-3z+5\bar{z}}\right) : z ∈ C, Re(z)=3 \right)$ is equal to the interval (α,β), then 24(β-α) is equal to

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

Negation of (p⇒q)⇒(q⇒p) is

For n ∈ N let $S_n$={z∈C:|z−3+2i|=$\frac{n}{4}$} and $T_n$={z ∈ C:|z−2+3i|=$\frac{1}{n}$}.Then the number of elements in the set

Let A = {n∈N : H.C.F. (n, 45) = 1} and
Let B = {2k :k∈ {1, 2, …,100}}. Then the sum of all the elements of $A∩B$ is ___________

Let
$f(x) = 2x^2 - x - 1\ and\ S = \{ n \in \mathbb{Z} : |f(n)| \leq 800 \}$
Then, the value of ∑_n∈S f(n) is equal to ________.

Let A,B,C be finite sets. Suppose that n(A)=10, n(B)=15, n(C)=20, n(A∩ B)=8 and n(B∩ C)=6. Then the possible value of n(A∪ B∪ C) is

Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of m and n respectively are:

Universal set:
\[ U = \{ x \mid x^5 - 6x^4 + 11x^3 - 6x^2 = 0 \} \]

Subsets:
\[ A = \{ x \mid x^2 - 5x + 6 = 0 \}, \quad B = \{ x \mid x^2 - 3x + 2 = 0 \} \]

Find: \[ (A \cap B)' \]

Let $A, B, C$ be finite sets. Suppose that $n(A) = 10$, $n(B) = 15$, $n(C) = 20$, $n(A \cap B) = 8$, and $n(B \cap C) = 9$. Then the possible value of $n(A \cup B \cup C)$ is

Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n respectively are:

Universal set, \[ U=\{x\mid x^5-6x^4+11x^3-6x^2=0\}; \quad A=\{x\mid x^2-5x+6=0\}; \quad B=\{x\mid x^2-3x+2=0\}. \] What is $(A\cap B)'$?

The set $(A\setminus B)\cup(B\setminus A)$ is equal to:

Let A and B be two sets then $ (A \cup B) \cup (A \cap B) $ is equal to:

Let A=\x:x R, |x|<1 B=\x:x R, |x-1| 1 and A B=R-D, then the set D is

For any two statements

p

and

q

, the negation of the expression

p \lor (\sim p \land q)

is:

Let $S=x: x∈R$ and $\left(\sqrt{3}+\sqrt{2})^{x^2-4}+(\sqrt{3}-\sqrt{2})^{x^2-4}=10\right\}$Then $n(S)$ is equal to