Question

If A and B are two sets such that n(A – B) = 24 , n(B – A) = 19 and n(AՈB) = 11

Find

i. n(A U B)

ii. n(B)​

Answer 1

Step-by-step explanation:

n(A)=n(A-B)+n(AnB)

=24+11

=35

n(B)=n(B-A)+n(AnB)

= 19+11

=30

n(AUB)= n(A)+n(B)-n(AnB)

= 35+30-11

=54

Answer 2

Answer:

Concept:

  A set is a group of things. A set's elements or members are the objects that make up the set. Any kind of item, including sets, can be one of the elements in a set. A set's components don't even need to be of the same type.

Step-by-step explanation:

• A group of real numbers called an interval are all real numbers that fall between two real numbers. Whether the interval is open, closed, or half-open determines whether the endpoints should be included or excluded.

• A set that has no elements is said to be empty.

• Capital letters are used to denote the set. Some other kinds of sets include the infinite set, the finite set, the equivalent set, the subset, the universal set, and the superset. Each kind of set has a different place in calculations

Given:

A and B are two sets such that n(A – B) = 24 , n(B – A) = 19 and

n(AՈB) = 11.

To find:

n(A U B) , n(B)​.

Solutions:

n(A) = n(A-B) + n(A∩B)

      = 24+11

      = 35

n(B) = n(B-A) + n(A∩B)

      = 19+11

      =30

n(AUB) = n(A) +n(B) -n(A∩B)

            = 35+30-11

            = 54

Hence the value of  (1) n(AUB) = 54

                                 (2) n(B) = 30

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