List of top Mathematics Questions on Operations on Sets

Let the sets A and B denote the domain and range respectively of the function \(f(x)=\frac{1}{\sqrt[x]-x}\) where [x] denotes the smallest integer greater than or equal to x . Then among the statements 
(S1) : A ∩ B = (1, ∞) – N and  
(S2) : A ∪ B = (1, ∞) 

Let A be a set containing n elements, A subset P of A is chosen and set A is reconstructed by replacing the elements of P. A subset Q of A is chosen again. The number of ways of choosing P and Q such that Q contains just one element more than P is

If A and B are disjoint sets and \(n(A)=4\) ,\(n(A∪B)=7\), then the value of \(n(B)\) is

If A= {P,O,L,Y,T,E,C,H,N, I} and B = {E, X, A, M}, then \(A∩B =\)

If A = {1, 2, 3, 4, 5} and B={4, 5, 6, 7} then A-B=__

Let A,B,C are subsets of set X. Then consider the validity of the following set theoretic statement:

The number of elements in the set S= {x∈R : 2cos⁡\((\frac{x_2+x}{6})\)=\(4^x+4^{-x}\)}

Which of the following statement is a tautology?

Let S = {E₁, E₂, ……………., E₈} be a sample space of a random experiment such that \(P(E_n) = \frac{n}{36}\) for every n = 1, 2, ………, 8. Then the number of elements in the set\(\{ A \subseteq S : P(A) \geq \frac{4}{5} \}\) is_________.

If A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. then, I. P(not A) = 0.58 II. P(not B) = 0.52 III. P(A or B) = 0.47

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

The set of all real numbers x for which $x^2-|x+2|+x>0$ is

Let $R$ be a relation on $R$, given by $R=\{(a, b): 3 a-3 b+\sqrt{7}$ is an irrational number $\}$Then $R$ is

Two finite sets $A $ and$ B $ have m and n elements respectively. If the total number of subsets of $A $ is 112 more than the total number of subsets of $B$, then the value of m is

Two finite sets have $m$ and $n$ elements. The total number of subsets of the first set is $56$ more than the total number of subsets of the second set. The values of $m$ and $n$ are