Question

Please solve class 11 ..sets ☺​
any brainly star here

Answer 1

Answer.

$n(B)=25$, $n(A\cup B)=35$

Answer Keys.

The Benn diagram is attached. Please view it.

According to the Benn diagram,

• $n(A\cup B)=n(A)+n(B)-n(A\cap B)$
• $n(B)=n(B-A) +n(A\cap B)$

Solution.

For the first value,

$n(B)$

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

$=20+5=\boxed{25}$

For the second value,

$n(A\cup B)$

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

According to the Benn diagram, we can simplify it further.

$=\{n(A-B)+n(A\cap B)\}+\{n(B-A)+n(A\cap B)\}-n(A\cap B)$

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

$=10+20+5=\boxed{35}$

More information.

The Benn diagram comes in handy in calculations of sets. It is a powerful tool as you can show the property of sets, without set calculations. So, it is good for you to get used to it.