State True or False:  $(A\cup B)'=A'\cap B'$

For any two sets A and  B $A-(B\cup C)=(A-B)\cap (A-C)$

$AB=A$ and $BA=B$, then which of the following is not true?

For any two sets  A and B $A\cup B=A\cap B$ if A$=$B.

If $A$ and $B$ are subsets of $U$ such that $n(U) = 700, n(A) = 200, n(B) = 300, n$$\displaystyle \left ( A\cap B \right )$ $= 100$, then find $n\displaystyle \left ( A'\cap B' \right )$

If A has 5 elements and B has 8 elements such that $\displaystyle A\subset B,$ then the number of elements in $\displaystyle A\cap  B,$ and $\displaystyle A\cup  B,$ are respectively :

While preparing the progress reports of the students, the class teacher found that $70$% of the students passed in Hindi, $80$% passed in English and only $65$% passed in both the subjects. Find out the percentage of students who failed in both the subjects

In a science talent examination, $50$% of the candidates fail in Mathematics and $50$% fail in Physics. If $20$% fail in both these subjects, then the percentage who pass in both Mathematics and Physics is

$(A\cup B)^{'} = A^{'} \cap B^{'}$ is called ____________ law.

In a survey, it was fond that $65$% of the people watched news on TV, $40$% read in newspaper, $25$% read newspaper and watched TV. What percentage of people neither watched TV nor read newspaper?

Comment true or false  on the following statements
$ A\cap \left( B-C \right) =\left( A\cap B \right) -\left( A\cap C \right)$

A survey on a sample of $25$ new cars being sold at a local auto dealer was conducted to see which of the three popular options - air-conditioning, radio and  power windows - were already installed.
The survey found:
$15$ had air-conditioning
$2$ had air-conditioning and power windows but no radios.
$12$ had power windows
$6$ had air-conditioning and radio but no power windows.
$11$ had radio.
$4$ had radio and power windows.
$3$ had all three options.
What is the number of cars that had none of the options?

With usual notations $n\left( A\cup B\cup C \right) =20,n\left( A\cap B\cap C\prime  \right) =2,n\left( B\cap C\cap A\prime  \right) =n\left( A\cap C\cap B\prime  \right) =4\quad$

Let $n(u)=700,n(A)=200,n(B)=300$
$n\left( A\cap B \right) =100,n\left( A^{\prime} \cap B^{\prime}  \right) =$

A - (A - B) =$ A  \cap \, B $

The value of $(A\cup B\cup C)\cap {(A\cap {B}^{c}\cap {C}^{c})}^{c}\cap {C}^{c}$

Given that the universal set,$ \xi =$ {x : 1 < x < 12 and x is an integer} and the sets P = {x : x is a prime number}, Q = {x : x is a multiple of 4} and R = {2, 3, 8, 9} the elements of the set $(Q \cup R)' \cap P$ are:

$(A'-B) \cup (B-A)=$

if $X' = Y$ then $\displaystyle \left (X \cap Y  \right )'$ is equal to 

If among natural numbers $A={5,6,7}$ and $B={8,9,10}$ , then 

Given $A={x\in N :x<6} ,B={3,6,9}$ and $C={x \in N: 2x-5\le 8}$

If $A, B$ be any two sets, then $(A\cup B)'$ is equal to

If $U = {3, 4, 5, 6, 7, 8, 9}, X = {3, 4}, Y = {5, 6}$ and $Z = {7, 8, 9}$, then $\displaystyle Y'\cap \left ( X\cap Z \right )'$ is equal to 

If $U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}$, $A = {0, 3, 4, 7}$ ,$B = {1, 2, 8, 9}$
then $(A U B)'$ is

Out of 800 boys in a school 224 played cricket, 240 played hockey and 236 played basketball. Of the total 64 played both basketball and hockey, 80 played cricket and basketball and 40 played cricket and hockey, 24 players all the three games. The number of boys who did not play any game is

Find the De Morgan's law of intersection.

Find the De Morgan's law of union.

In order to draw a graph of $f(x) = ax^{2} + bx + c$, a table of values was constructed. These values of the function for a set of equally spaced increasing values of $x$ were $3844, 4096, 4227, 4356, 4489, 4624$, and $4761$. The one which is incorrect is

$(A\cup B)' $  $=$

Let the universal set, $\xi$ = {$x : 1 \leq  x \leq  15$ and x is an  integer} set H = {x : x is a multiple of 3} and set K = {x : x is an even number}. Find $n(H' \cap K)$.