Question

Suppose Set B contains 49 elements and the total number elements in either Set A or Set B is 100. If the Sets A and B have 31 elements in common, how many elements are contained in set A?

Answer 1

`82`

Step-by-step explanation:

Mathematically:

`n(A\text{ or B\rparen = \lparen n\lparen A\rparen - \lparen n\lparen AnB\rparen\rparen +\lparen n\lparen B\rparen - n\lparen A n B\rparen\rparen + n\lparen A n B\rparen}`

We have the substitution as:

Let us call n(A) x

`100\text{ = \lparen x-31\rparen+}(49-31)\text{ + 31}`

Solving for x, we have it that:

`\begin{gathered} 100\text{ = x-31 +49 - 31 +31} \\ 100\text{ = x-31+18+31} \\ 100\text{ = x+18} \\ x\text{ = 100-18} \\ x\text{ = 82} \end{gathered}`