Set theory practice · Easy

Let S = {1, 2, 3, … , 100}. The number of non – empty subsets A of S such that the product of elements in A is even, is

Let $S=\left\{x \in[-6,3]-\{-2,2\}: \frac{|x+3|-1}{|x|-2} \geq 0\right\}$ and $T=\left\{x \in Z: x^2-7|x|+9 \leq 0\right\}$. Then the number of elements in $S \cap T$ is

Let $A$ be a set containing 10 distinct elements, the total number of distinct functions from $A$ to $A$ is

Given $n\left( U \right) = 20,\;n\left( A \right) = 12,\;n\left( B \right) = 9,n\left( {A \cap B} \right) = 4$, where $U$ is the universal set, $A$ and $B$ are subsets of $U$, then $n\left[ {{{\left( {A \cup B} \right)}^c}} \right]$ equals to

Let $n\left( \mathcal{U} \right) = 700,\;n\left( A \right) = 200,\;n\left( B \right) = 300$ and $n\left( {A \cap B} \right) = 100.$ Then, $n\left( {{A^c} \cap {B^c}} \right) =$

Which of the following collection is a set?

Consider the following statements.

I. $\phi \in\{\phi\} \quad$ II. $\{\phi\} \subseteq \phi$

Which of the statements given above is/are correct?

Suppose $A_1, A_2, A_3, \ldots \ldots \ldots, A_{30}$ are thirty sets each having 5 elements and $B_1, B_2, \ldots \ldots ., B_n$ are $n$ sets each with 3 elements. Let $\bigcup_{i=1}^{30} A_i=\bigcup_{j=1}^n B_j=S$ and each elements of $S$ belongs to exactly 10 of the $A_i^{\prime} s$ and exactly 9 of the $B_j^{\prime} s$. Then $n$ is equal to:

${X}$ and ${Y}$ are two sets such that $n({X})=17, n({Y})=23$, $n({X} \cup {Y})=38$ then $n({X} \cap {Y})$ is

The set $(A \backslash B) \cup(B \backslash A)$ is equal to

In a class of 60 students, 34 have passed in Mathematics and 38 in physics. If each of the students pass at least in one of the subjects, then the number of students who have passed in physics only is

Universal set, $U = \left\{ {x:{x^5} - 6{x^4} + 11{x^3} - 6{x^2} = 0} \right\}$ And $A = \left\{ {x:{x^2} - 5x + 6 = 0} \right\}$
$\;B = \left\{ {x:{x^2} - 3x + 2 = 0} \right\}$
Then, ${\left( {A \cap B} \right)^\prime }$ is equal to

If $A, B, C$ be three sets such that $A \cup B=A \cup C$ and $A \cap B=A \cap C$, then

Let $A$ and $B$ two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$ then

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 $(A \cup B)^{\prime} \cup\left(A^{\prime} \cap B\right)=$

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

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

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

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?

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?

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

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

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