Operations on Sets

For any two sets $A$ and $B$, $A-\left(A-B\right)$ is equal to

Let $A$ be te set of non-negative integers, $I$ is the set of integers, $B$ is the set of non-positive integers, $E$ is the set of even integers and $P$ is the set of prime numbers then

Let $A=\left\{0, 1, 2, 3, 4\right\}$, $B=\left\{x\in N|x\le 20\right\}$, $C=\left\{x\in N|x>3\right\}$, $D=\left\{x\in N| x \mathrm{is} \mathrm{divisible} \mathrm{by} 7\right\}$.

Determine $A\cup B$

A college awarded $38$ medals in football, $15$ in basketball and $20$ in cricket. If these medals went to a total of $58$ men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports ?

If $X$ and $Y$ are two sets such that $X\cup Y$ has $50$ elements, $X$ has $28$ elements and $Y$ has $32$ elements, how many elements does $X\cap Y$ have ?

Suppose that in a certain exam, $200$ students appear for Mathematics, $50$ appear for physics, $100$ appear for Chemistry, $20$ appear for Mathematics & Physics, $60$ appear for Mathematics & Chemistry, $35$ appear for Physics & Chemistry, while $245$ appear for either Mathematics or Physics or Chemistry.

Determine the number of students who appear for

(i) All 3 subjects

(ii) Exactly for one of the subjects

Use Venn Diagram to find the same.

If $n\left(P\right)=12, n\left(M\right)=12$ and $n\left(M\cap P\right)=4$ then $n\left(M\cup P\right)=$

Let $A=\left\{1,2,3,4,5,6,7\right\}$. Define $B=${$T\subseteq A$: either $1\notin T$ or $2\in T$} and $C=${$T\subseteq A:T$ the sum of all the elements of $T$ is a prime number.} Then the number of elements in the set $B\cup C$ is _____.

If $A$ and $B$ are two smallest sets such that $A\cup \left\{1\right\}=\left\{1,2,3,4\right\}$ and $B\cup \left\{5\right\}=\left\{4,5,6,7,8\right\}$. If $P=A-B$ and $Q=B-A$, then the number of relation from $P$ to $Q$ is

Given, $n\left(A\right)=14, n\left(B\right)=10$ and $n\left(A\cap B\right)=18,$ then find $n\left(A\cup B\right).$

Let $U$ be a universal set and $n\left(U\right)=12$. If $A,B\subset U$ such that $n\left(B\right)=6$ and $n(A\cap B)=2$ then $n(A\cup B^c)$ is equal to

For any sets $A$ and $B$, show that $P\left(A\cap B\right)=P\left(A\right)\cap P\left(B\right)$.

Show that $A\cup B=A\cap B$ implies $A=B$

Let $A=\left\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\right\}$ and $B=\left\{2, 3, 5, 7\right\}$. Find $A\cap B$ and hence show that $A\cap B=B$.

Let $X=\{$ Ram, Geeta, Akbar } be the set of students of Class $XI$, who are in school hockey team. Let $Y=\{$ Geeta, David, Ashok$\}$ be the set of students from Class $XI$ who are in the school football team. Find $X\cap Y$.

Let $A=\left\{2, 4, 6, 8\right\}$ and $B=\left\{6, 8, 10, 12\right\}$. Find $A\cap B$.

Let $X=$$\{$ Ram, Geeta, Akbar $\}$ be the set of students of Class $XI$, who are in school hockey team. Let $Y=$$\{$ Geeta, David, Ashok $\}$ be the set of students from Class $XI$ who are in the school football team. Find $X\cup Y$ and interpret the set.

Let $A=\left\{a, e, i, o, u\right\}$ and $B=\left\{a, i, u\right\}$. Show that $A\cup B=A$.

Let $A=\left\{2, 4, 6, 8\right\}$ and $B=\left\{6, 8, 10, 12\right\}$. Find $A\cup B$.

Prove that union of countable sets is countable.