In a class of 100 students, 70 like math, 60 like physics, and 50 like both. How many students don’t like either subject?

To solve this problem, we can use the principle of inclusion and exclusion. Let set A be the students who like math, set B be the students who like physics, and let set C be the students who like both.

We know that:

1. |A| = 70 (70 students like math)

2. |B| = 60 (60 students like physics)

3. |A ∩ B| = 50 (50 students like both)

Using the principle of inclusion and exclusion, the total number of students who like math or physics or both is:

|A ∪ B| = |A| + |B| − |A ∩ B|

So in our case:

|A ∪ B| = 70 + 60 − 50 = 80

Now, we know that there are 100 students in total, and 80 of them like either math, physics, or both. Thus, the number of students who don’t like either subject is:

100 − 80 = 20

Hence, 20 students don’t like either math or physics.