In a group of 25 boys, 18 like Association Football whilst 14 like Rugby Football. How many like both kinds of football?
To find out how many boys like both kinds of football, we need to use the concept of set intersection.
Given that there are 18 boys who like Association Football and 14 boys who like Rugby Football, we can represent these two sets as follows:
Set A: Boys who like Association Football = {18}
Set B: Boys who like Rugby Football = {14}
To find the intersection, we need to find the common elements between these two sets. In other words, we need to find how many boys are present in both sets.
Using the formula for set intersection, we can determine the number of boys who like both kinds of football:
Number of boys who like both kinds of football = |A ∩ B|
Here, the symbol "∩" represents the intersection of the two sets, and "A ∩ B" represents the common elements between set A and set B.
Substituting the values into the formula, we get:
Number of boys who like both kinds of football = |{18} ∩ {14}|
Since both sets have only one element each, we can see that the common element is the same in both sets.
Therefore, the number of boys who like both kinds of football is 1.