List of top Mathematics Questions on Set Theory asked in NIMCET

A researcher found that 70% of people who own a cat also own a dog, but only 20% of dog owners also own a cat. If there are 1,001 dog owners, how many cat owners are there?

Which of the following is not same as $(A\Delta B)\cap C$?

There are two sets $A$ and $B$ with $|A|=m$ and $|B|=n$. If $|P(A)|-|P(B)|=112$, choose the wrong option.

A survey is done among 200 people. 60% like tea and 72% like coffee. Let $x$ be the number who like both. Let $m\le x\le n$. Find the correct option.

If $A \subseteq B$ and $B \subseteq C$, then cardinality of $A \cup B \cup C$ is equal to:

Let $ A = (1, 2, 3, \dots, 20) $. Let $ R \subseteq A \times A $ such that $ R = \{(x, y) : y = 2x - 7 \} $. Then the number of elements in $ R $ is equal to:

Let $A = \{5n - 4n - 1 : n \in \mathbb{N}\}$ and $B = \{16(n - 1): n \in \mathbb{N}\}$ be sets. Then:

Out of a group of 50 students taking examinations in Mathematics, Physics, and Chemistry, 37 students passed Mathematics, 24 passed Physics, and 43 passed Chemistry. Additionally, no more than 19 students passed both Mathematics and Physics, no more than 29 passed both Mathematics and Chemistry, and no more than 20 passed both Physics and Chemistry. What is the maximum number of students who could have passed all three examinations?

Let $ Z $ be the set of all integers, and consider the set $ X = \{(x, y): x^2 + 2y^2 = 3, x, y \in Z $ and $ Y = \{(x, y): x>y, x, y \in Z\} $. Then the number of elements in $ X \cap Y $ is:

Let $ R $ be a reflexive relation on the finite set $ A $ having 10 elements and if $ m $ is the number of ordered pairs in $ R $, then

Let A and B be sets. \[A \cap X = B \cap X = \varnothing \quad \text{and} \quad A \cup X = B \cup X \quad \text{for some set } X,\ \text{find the relation between } A \text{ and } B.\]

A survey is done among a population of 200 people who like either tea or coffee. It is found that 60% of the population like tea and 72% of the population like coffee. Let x be the number of people who like both tea & coffee. Let $ m \leq x \leq n $, then choose the correct option.

There are two sets A and B with $ |A| = m $ and $ |B| = n $. If $ |P(A)| - |P(B)| = 112 $ then choose the wrong option (where $ |A| $ denotes the cardinality of A, and P(A) denotes the power set of A)