Question

Suppose that the number of elements in set A is n open parentheses A close parentheses equals 80 space a n d space n open parentheses B close parentheses equals 50 space a n d space t h e space n open parentheses A union B close parentheses equals 95 find the number of elements in n open parentheses A intersection thin space B close parentheses

Answer 1

Given:

Suppose that the number of elements in set A is

n open parentheses A close parentheses equals 80 space a n d

space n open parentheses B close parentheses equals 50 space

a n d space t h e space n open parentheses A union B close parentheses equals 95

To find:

Find the number of elements in n open parentheses A intersection thin space B close parentheses.

Solution:

From given, we have,

n open parentheses A close parentheses equals 80

⇒ n (A) = 80

n open parentheses B close parentheses equals 50

⇒ n (B) = 50

n open parentheses A union B close parentheses equals 95

⇒ n (A ∪ B) = 95

We use the below formula to find, n open parentheses A intersection thin space B close parentheses.

⇒ n (A ∩ B) = ?

⇒ n (A ∪ B) = n (A) + n (B) - n (A ∩ B)

95 = 80 + 50 - n (A ∩ B)

95 = 130  - n (A ∩ B)

n (A ∩ B) = 130 - 95

∴ n (A ∩ B) = 35.

n open parentheses A intersection thin space B close parentheses equals 35.