Complement of a Set

If the universal set $U=\left\{1,2,3,4,5,6,7\right\}$ and $A=\left\{1,2,3,4\right\}$ then verify that $\left(A\text{'}\right)\text{'}=A$

If the universal set $U=\left\{1,2,3,4,5,6,7\right\}$ and $A=\left\{1,2,3\right\}$ then verify that $\left(A\text{'}\right)\text{'}=A$

Given $n\left(U\right)=20,n\left(A\right)=12,n\left(B\right)=9,n(A\cap B)=4$, where $U$ is the universal set, $A$ and $B$ are subsets of $U$, then find $n\left(\left(A\cup B\right){}^C\right)$.

Let $U$ be the universal set for $A$ and $B$, where $B$ is complement set of $A$.

If $n\left(A\right)=4$ and $n\left(U\right)=11$ then find $n\left(B\right)$

Let $\mathrm{U}=\{a,b,c,d,e,f,g,h\};$ find the complement of the set $\mathrm{C}=\left\{a,c,e,g\right\}$

Let $U=\{a,b,c,d,e,f,g,h\}$. Then, find the complement of the set $B=\left\{d,e,f,g\right\}$.

Let $U=\{a,b,c,d,e,f,g,h\};$ find the complement of the set $A=\left\{a,b,c\right\}$

If $B=[2,6]$ and $C=[4,9]$ Then find $B^{\text{'}}\cap C^{\text{'}}$

If $A=(-7,3]$, $B=[2,6]$ , then find $A^{\text{'}}\cap B$

If $A$and $B$ are subsets of a universal set $X$ and $n\left(X\right)=50, n\left(A\right)=35, n\left(B\right)=20, n\left(A^{\text{'}}\cap B^{\text{'}}\right)=5$

Find $n\left(A\cap B\right)$

If $A$and $B$ are subsets of a universal set $X$ and $n\left(X\right)=50, n\left(A\right)=35, n\left(B\right)=20, n\left(A^{\text{'}}\cap B^{\text{'}}\right)=5$. find $n\left(A\cup B\right)$

If $A$ and $B$ are two sets such that $n\left(A\right)=8, n\left(B\right)=11$ and $n(A\cup B)=14$, then find $n(A\cap B).$

If $A$ and $B$ are two sets such that $n(A-B)=24, n(B-A)=19$ and $n(A\cap B)=11$. Find $n\left(B\right)$.

If $A$ and $B$ are two sets such that $n\left(A\right)=37, n\left(B\right)=26$ and $n(A\cup B)=51,$ find $n(A\cap B)$.

Let $U=\{0, 1, 2, 3, 4, 5, 6, 7\}, A=\{1, 3, 5, 7\}$ and $B=\{0, 2, 3, 5, 7\},$ find the number of elements in a set $A^{\text{'}}$.

If $U=\{a, b, c, d, e, f, g, h\}, A=\{b, d, f, h\}$ and $B=\{a, d, e, h\},$ find the number of element in set $B^{\text{'}}$.

If $U$ is the universal set and $A\subset U$, then $n\left(A\cap A^{\text{'}}\right)=$_____.

If $U$ is the universal set and $A\subset U$ then $A\cup A^{\text{'}}=$_____

In a school, there are $20$ teachers who teach Mathematics or Physics. Of these, $12$ teach Mathematics and $4$ teach both Physics and Mathematics. How many teach Physics?

If $X$ and $Y$ are two sets such that $X$ has $40$ elements, $X\cup Y$ has $60$ elements and $X\cap Y$ has $10$ elements, how many elements does $Y$ have?