Question

for any sets A and B ,if n(A)=15 and n(B) =10,then the sum of maximum and minimum values of n(A U B) is equal to​

Answer 1

Answer:

MXimum value of n(A U B) is 25

Minimum value of nA U B) IS 15

Answer 2

Given:

• n(A)=$15$
• n(B)=10

To find:

• The maximum and minimum values of n(A ∪ B).

Step-by-step explanation:

• We know that set A has $15$ elements.
• It is also given that set B has $10$ elements.
• There is a condition to find the minimum A ∪ B elements.
• The condition is : Out of $15$ elements of set A, $10$ elements are identical to that of set B.
• In this case,

        A ∪ B $=$ B

• So it will have $15$ elements.
• And there is also a condition for the maximum A ∪ B elements.
• The condition is: A and B is disjoint set, that mean there will no common element in them.
• Then,

        n(A ∪ B) $=$ n(A) $+$ n(B)

• Therefore,

        n(A ∪ B) $=$ $15+10$

• By solving we get,

        n(A ∪ B) $= 25$

Final answer:

• The maximum value of n(A ∪ B) is $25$.
• The minimum value of n(A ∪ B) is $15$.