in one elementary school class the following information on sports preferences was obtained: 7 liked tennis; 11 liked baseball; 9 liked soccer; 5 liked tennis and baseball; 3 liked baseball and soccer; 2 liked tennis and soccer; and 2 liked all three sports. How many students liked either tennis or soccer?

Hint:

Draw a Venn diagram to fill in all the numbers, starting with the last (2 liked all sports) and work backwards.
I find 17 students in all.

Not too sure how the question is supposed to be interpreted:
1. how many students liked tennis and no other sport or soccer and no other sport? (5)
2. how many students liked at least one of tennis or soccer? (13)

14

13

To find out how many students liked either tennis or soccer, we need to add the number of students who liked tennis and soccer separately and then subtract the number of students who liked all three sports (as they have already been counted twice).

Let's break down the given information:
- 7 liked tennis
- 11 liked baseball
- 9 liked soccer
- 5 liked tennis and baseball
- 3 liked baseball and soccer
- 2 liked tennis and soccer
- 2 liked all three sports

First, let's calculate the number of students who liked both tennis and soccer by adding the number of students who liked tennis and soccer together:

7 (tennis) + 2 (tennis and soccer) = 9 students liked tennis or soccer (including those who liked both)

Next, let's calculate the number of students who liked either tennis or soccer by adding the number of students who liked each sport separately:

9 (tennis or soccer) + 11 (baseball) = 20 students liked either tennis or soccer or both

However, we have counted the 2 students who liked all three sports twice in the above calculation, so we need to subtract them:

20 (tennis or soccer or both) - 2 (tennis + baseball + soccer) = 18 students liked either tennis or soccer

Therefore, the number of students who liked either tennis or soccer is 18.