Set theory practice · Mixed difficulty

A class has 175 students. The following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. Hoe many students have offered Mathematics alone?

Let $A$ and $B$ be two sets. The $(A \cup B)^{\prime} \cup\left(A^{\prime} \cap B\right)=$

If $A=\{5 n / n \in \mathbb{N}, n \leq 100\}, B=\{3 n / n \in \mathbb{N}, n \geq 100\}$ and $C=\{2 n / n \in \mathbb{N}\}$ then number of elements in $(A \cap B) \cap C^1$ is

Let ${R}$ be the set of real numbers, If $f: {R} \rightarrow {R}$ is defined by $f(x)=e^x$, then $f$ is

Which of the following is true?

Let $A=\{x:|x|<2\}$ and $B=\{x:|x-2| \geq 3\}$. Then

Let $X$ and $Y$ be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then,$n\left( {X \cap Y} \right)$ is equal to

Which of the following is not correct?

If $A = \left\{ {1,3,5,7,9,11,13,15,17} \right\},B = \left\{ {2,4 \ldots ,18} \right\}$ and $N$ is the universal set, then $A' \cup \left( {\left( {A \cup B} \right) \cap B'} \right)$ is

Let $n(\mathrm{U})=700, n(\mathrm{A})=200, n(\mathrm{B})=300, n(\mathrm{A} \cap \mathrm{B})$ $=100$, then $n\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)$ is equal to

In a city, three daily newspapers $A, B, C$ are published. $42 \%$ of the people in that city read $A$, $51 \%$ read $B$ and $68 \%$ read C. $30 \%$ read ${A}$ and ${B} ; 28 \%$ read ${B}$ and ${C}$; $36 \%$ read ${A}$ and ${C} ; 8 \%$ do not read any of the three newspapers. The percentage of persons who read all the three papers is

Let ${A_1},{A_2},{A_3} \ldots ,{A_{100}}$ be 100 sets such that $n\left( {{A_i}} \right) = i + 1$ and ${A_1} \subset {A_2} \subset {A_3} \subset \ldots \subset {A_{100}},$ then $U_{i = 1}^{100}{A_i}$ contains… elements

In a certain town, $25 \%$ of the families own a phone and $15 \%$ own a car; $65 \%$ families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements:
(A) $5 \%$ families own both a car and a phone
(B) $35 \%$ families own either a car or a phone
(C) 40,000 families live in the town
Then,

If $A=\{x: x=2 n+1, n \in Z\} \quad$ and $B=\{x: x=2 n, n \in Z\}$, then $A \cup B=$

If $\left.X=\left\{8^n-7-1: n \in N\right): n \in N\right\}$ and $Y=\{49(n-1): n \in N\}$ then:

In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many persons like both coffee and tea?

If $A,B$ and $C$ are three sets such that $A \supset B \supset C,$ then $\left( {A \cup B \cup C} \right) - \left( {A \cap B \cap C} \right) =$

From 50 students taking examinations in Mathematics, Physics and Chemistry, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 passed Mathematics and Chemistry and at most 20 passed Physics and Chemistry. The largest possible number that could have passed all three examinations is

Let ${P}$ be a set of squares, ${Q}$ be set of parallelograms, ${R}$ be a set of quadrilaterals and ${S}$ be a set of rectangles. Consider the following:

I. ${P} \subset {Q} \quad$ II. ${R} \subset {P} \quad$ III. ${P} \subset {S} \quad$ IV. ${S} \subset {R}$

Which of the above are correct?

Let $A$ and $B$ be two sets, then $(A \cup B)^{\prime} \cup\left(A^{\prime} \cap B\right)$ is equal to

If $R$ and $R^{\prime}$ are symmetric relations (not disjoint) on a set $A$, then the relation $R \cap R^{\prime}$ is

If $P(A)$ denotes the power set of $A$ and $A$ is the void set, then what is number of elements in $P\{P\{P\{P(A)\}\}\} ?$

${X}$ and ${Y}$ are two sets such that ${X}$ has 40 elements, ${X} \cup$ ${Y}$ has 60 elements and ${X} \cap {Y}$ has 10 elements, then number of elements ${Y}$ has

If there are three atheletic teams in a school, 21 are in the basketball team, 26 in hockey team and 29 in the football team. 14 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the games. The total number of members is

If $\mathrm{A}$ and $\mathrm{B}$ are two sets, then $(\mathrm{A}-\mathrm{B}) \cup(\mathrm{B}-\mathrm{A})$ $\cup(A \cap B)$ is equal to

Let $P$ be the set of prime numbers and $S=\left\{t: 2^t-1\right.$ is a prime\}. Then,

Out of 800 boys in a school 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game is

Let $Z$ denote the set of integers, then
$\left\{ {x \in Z:\left| {x - 3} \right| < 4} \right\}n\left\{ {x \in Z:\left| {x - 4} \right| < 5} \right\} =$

Suppose $A_1, A_2, A_3, \ldots \ldots . A_{30}$ are thirty sets each with 5 elements and $B_1, B_2, B_3, \ldots \ldots . B_n$ are n sets. Each with three elements such that $\mathop U\limits_{i = 1}^{30} A_i=\mathop U\limits_{j = 1}^{n} B_j=S$. If each element of ${S}$ belongs to exactly 10 of the $A_i$ 's and exactly 9 of the $B_j$ 's, then the value of ${n}$ is

Let $A=\{1,2,3\}, B=\{3,4\}$ and $C=\{4,5,6\}$, then $A \cup(B \cap C)$ is