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?
Accepted Solution
A:
Answer: a) 4, b) 13 and c) 17Step-by-step explanation:Since we have given that Number of elements in A = 9Number of elements in B = 4a) 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 = Фn(A∩B) = 0So, it becomes,[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)\\\\n(A\cup B)=9+4-0\\\\n(A\cup B)=13[/tex]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=17Hence, a) 4, b) 13 and c) 17