Club R has 11 members and Club T has 16 members. If a toatal of 20 people belong to the two clubs, how many people belong to both clubs?
To find the number of people who belong to both clubs, you can use a method called the intersection of sets. We know that Club R has 11 members and Club T has 16 members. Let's represent the membership of each club as sets:
Let set R represent the members in Club R. |R| = 11
Let set T represent the members in Club T. |T| = 16
To find the intersection, we need to find the common members between the two sets. Mathematically, this can be represented as:
|R ∩ T| = |R| + |T| - |R U T|
Where |R ∩ T| represents the size of the intersection of sets R and T, and |R U T| represents the size of the union of sets R and T.
Given that a total of 20 people belong to the two clubs, we can substitute the values into the formula:
|R ∩ T| = 11 + 16 - 20
Simplifying further:
|R ∩ T| = 27 - 20
|R ∩ T| = 7
Therefore, there are 7 people who belong to both Club R and Club T.