Tag: mathematics and statistics

$n(A\Delta B)=n(A)+n(B)-n(A\cap B)$

Here we don`t know the $n(A\cap B)$

So the answer cannot be Determined.

$A$ is the first  element in  the cartesian product $A\times B=\left{a\,,b\,,a\,,b\,,a\,,b\right}$

x has to be 3 and y has to be 5.

By rule of ordered pairs this statement is true.

Given, $n\left( A \right) =4$ and $n\left( B \right) =5$ 

Product of two sets is the set of ordered pairs formed by mapping every element from the first set to every element of the second set.

So, $ A \times B = $ { $ (1,2), (1,3), (1,4), (2,2), (2,3), (2,4) $ }

And $ B \times A = $ { $ (2,1), (2,2), (3,1), (3,2), (4,1), (4,2) $ }

Clearly, $ A \times B \neq B \times A $

Given $n(A)=3,$  and $n(B) =3$
Hence $n(A\times B) = 3\times 3=9$

If $A$ and $B$ are any two non-empty sets.
then $A\times B$$=\left{(x,y):x\in A  and  y\in B\right}$
As $A = \left{2,3\right}$ and $B = \left{1,2\right}$
$A \times B$$=\left{(2,1), (2,2), (3,1), (3,2)\right}$
Hence, option A.

$\displaystyle A=\left{ 2,4,5 \right} ,B=\left{ 7,8,9 \right} $

$n(A\times B)=n(A)\times n(B)$