Question

consider the venn diagram below.

n(a) =

n(b)=

n(a ∩ b)=

n(a ∪ b)=

n(a)=

n(b)=

Explanation:

Step1: Find $n(A)$

The elements in set $A$ are the elements in the circle labeled $A$. So $n(A)=10 + 3=13$.

Step2: Find $n(B)$

The elements in set $B$ are the elements in the circle labeled $B$. So $n(B)=3 + 4 = 7$.

Step3: Find $n(A\cap B)$

The intersection $A\cap B$ is the common - part of $A$ and $B$. So $n(A\cap B)=3$.

Step4: Find $n(A\cup B)$

The union $A\cup B$ is all the elements in $A$ or $B$. So $n(A\cup B)=10+3 + 4=17$.

Step5: Find $n(A')$

The complement of $A$, $A'$, consists of elements not in $A$. So $n(A')=4 + 9=13$.

Step6: Find $n(B')$

The complement of $B$, $B'$, consists of elements not in $B$. So $n(B')=10+9 = 19$.

Answer:

$n(A)=13$
$n(B)=7$
$n(A\cap B)=3$
$n(A\cup B)=17$
$n(A')=13$
$n(B')=19$