If A and B are two sets such that  A union B  has 40 elements, A has 30 elements and B has 20 elements, how many elements does the shaded region have?

Asked by Topperlearning User | 31st Aug, 2016, 11:28: PM

Expert Answer:

                                                                   
  
 
Here, the shaded region represents the intersection of two sets A and B.
So, we have

n open parentheses A union B close parentheses space equals space n open parentheses A close parentheses plus n open parentheses B close parentheses minus n open parentheses A intersection B close parentheses

rightwards double arrow 40 space equals space 30 plus 20 minus n open parentheses A intersection B close parentheses

rightwards double arrow n open parentheses A intersection B close parentheses space equals space 10                

Answered by  | 1st Sep, 2016, 01:28: AM