To find the intersection of all three sports (soccer, rugby, and football), you need to consider the regions that are not labeled in the Venn diagram. In this case, as you mentioned, you have labeled the regions without information with letters: soccer only with 'a,' football only with 'b,' and the soccer and rugby intersection with 'c.'
To find the intersection of all three, you need to solve for the value of 'd.' Region 'd' represents the individuals who like soccer, rugby, and football.
Let's break down the given information and use it to find the value of 'd':
1. 4 liked only rugby: This means 'a' (soccer only), 'b' (football only), and 'c' (soccer and rugby) are not affected. So, we still have to account for 'd.'
2. 12 liked only rugby and football: This affects 'b' (football only) and 'c' (soccer and rugby). Thus, 'd' remains unaffected.
3. 63 did not like football: This statement does not directly affect 'd.'
4. 21 didn't like any: This statement also doesn't directly affect 'd.'
5. 16 liked only soccer and football: This affects 'a' (soccer only) and 'b' (football only), but 'd' remains unaffected.
6. 60 liked soccer: This statement affects 'a' (soccer only), but 'd' remains unaffected.
Based on the given information, we can conclude that 'd' represents the individuals who like soccer, rugby, and football. Hence, the intersection of all three is simply represented by 'd.'
To find the value of 'd,' we need to calculate it based on the information provided. You can start by adding up the counts of labeled regions 'a,' 'b,' and 'c' and subtracting this sum from the total count of individuals who liked soccer, rugby, or football (105).
d = Total count - (a + b + c)
= 105 - (a + b + c)
To find the specific values for 'd,' 'b,' 'c,' and 'a,' you might need additional information or equations.