Sets and Relations

In a class of 60 students, 45 students like music, 50 students like dancing, 5 students like neither. Then the number of students in the class who like both music and dancing is

Paragraph: Read the following information and answer: Consider the following Venn diagram, where $X, Y$ and $Z$ are three sets. Let the number of elements in $Z$ be denoted by $n(Z)$ which is equal to 90 . Question:…

Let $A=(x \in R:-1 \leq x \leq 1)$ and $S$ be the subset of $A \times B$, defined by $S=\left[(x, y) \in A \times B: x^2+y^2=1\right]$ Which one of the following is correct?

Consider the following in respect of sets A and B : $(\mathrm{A}-\mathrm{B}) \cup \mathrm{B}=\mathrm{A}$ $(\mathrm{A}-\mathrm{B}) \cup \mathrm{A}=\mathrm{A}$ $(A-B) \cap B=\phi$ $A \subseteq B \Rightarrow A \cup B=B$…

For any three non-empty sets $\mathrm{A}, \mathrm{B}, \mathrm{C}$ what is $(\mathrm{A} \cup \mathrm{B})-\{(\mathrm{A}-\mathrm{B}) \cup(\mathrm{B}-\mathrm{A}) \cup(\mathrm{A} \cap \mathrm{B})\}$ equal to?

$\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D are four sets such that $\mathrm{A} \cap \mathrm{B}=\mathrm{C} \cap \mathrm{D}=\phi$. Consider the following : $\mathrm{A} \cup \mathrm{C}$ and $\mathrm{B} \cup \mathrm{D}$ are…

Suppose there is a relation $*$ between the positive numbers x and y given by $\mathrm{x} * \mathrm{y}$ if and only if $\mathrm{x} \leq \mathrm{y}^2$. Then which one of the following is correct?

Let $S$ be a set of all distinct numbers of the form $\frac{\mathrm{P}}{\mathrm{Q}}$, where $\mathrm{p}, \mathrm{q} \in\{1,2,3,4,5,6\}$. What is the cardinality of the set S ?

Let $\mathrm{A}=\{1,2,3, \ldots 20\}$. Define a relation R from A to A by $\mathrm{R}=\{(x, y): 4 x-3 y=1\}$, where $x, y \in \mathrm{~A}$. Which of the following statements is/are correct? The domain of R is {1, 4, 7,…

Let R be a relation on the set N of natural numbers defined by ' $n R M \Leftrightarrow n$ is a factor of $m$ '. Then which one of the following is correct?

Let X be the set of all citizens of India. Elements $x, y$ in X are said to be related if the difference of their age is 5 years. Which one of the following is correct?

Consider the following statements in respect of sets : The union over intersection of sets is distributive. The complement of union of two sets is equal to intersection of their complements. If the difference of two…