Tag: complement of sets

If $U = \left {x|x\epsilon N, x < 5\right }, A = \left {x|x\epsilon N, x\leq 2\right }$ then $A' =$ __________.

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