Sets and Relations

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?

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: If…

Paragraph: In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 8 students who are good in both Hindi and Mathematics. 10 students…

Paragraph: A university awarded medals in basket ball, football and volleyball. Only $x$ students $(x \lt 6)$ got medal in all the three sports and the medals went to a total of $15 x$ students. It awarded $5 x$ medals…

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

In a state with a population of $75 \times 10^6, 45 \%$ of them know Hindi, 22% know English, 18% know Sanskrit, 12% know Hindi and English, 8% know English and Sanskrit, 10% know Hindi and Sanskrit and 5% know all the…

In a school, $50 \%$ students play cricket and $40 \%$ play football. If $10 \%$ of students play both the games, then what per cent of students play neither cricket nor football?

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: If…

If $A, B$ and $C$ are subsets of a given set, then which one of the following relations is not correct?

Let $A$ and $B$ be subsets of $X$ and $C=\left(A \cap B^{\prime}\right) \cup\left(A^{\prime} \cap B\right)$, where $A^{\prime}$ and $B^{\prime}$ are complements of $A$ and $B$ respectively in X . What is C equal to?

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:…