Question

Suppose Set A contains 52 elements and Set B contains 46 elements. If Sets A and B have 29 elements in common, what is the total number of elements in either Set A or Set B.

Answer 1

Answer: The number of elements in either Set A or Set B are 69

Explanation:

To calculate the number of elements present either in Set A or Set B, we use the equation:

$A\cup B=n(A)+n(B)-A\cap B$

where,

n(A) = number of elements present in Set A = 52

n(B) = number of elements present in Set B = 46

$A\cap B$ = Number of elements present in both Set A and Set B (intersection) = 29

$A\cup B$ = Number of elements in either Set A or Set B (union) = ?

Putting values in above equation, we get:

$A\cup B=52+46-29\\\\A\cup B=69$

Hence, the number of elements in either Set A or Set B are 69