Question

Let A and B be sets where |A1 = 9 and \B1 = 4. (a) What is the largest possible-value for (An BI?
(b) What is the largest possible value for AU BI?
(c) What is the value of AU BI+IAN B?

Answer 1

Answer: a) 4, b) 13 and c) 17

Step-by-step explanation:

Since we have given that

Number of elements in A = 9

Number of elements in B = 4

a) What is the largest possible value for A∩B.

Since B has only 4 elements.

So, As largest possible, it can be B⊆A.

So, Largest possible value for A∩B = 4

(b) What is the largest possible value for AUB?

If suppose A∩B = Ф

n(A∩B) = 0

So, it becomes,

$n(A\cup B)=n(A)+n(B)-n(A\cap B)\\\\n(A\cup B)=9+4-0\\\\n(A\cup B)=13$

So, the largest possible value for A∪B = 13

(c) What is the value of AU B+A∩B?

|A∪B|+|A∩B|=13+4=17

Hence, a) 4, b) 13 and c) 17