in a science class,65 student study physics while 40 study chemistry.if there are 93 student in the class,how many student study both physics and chemistry?

93=N(c)+N(p)-N(c,p)

93-65-40=-N(c,p)
N(c,p)=12

12

To find out how many students study both physics and chemistry, we need to use the concept of sets and their intersection.

1. First, we find the total number of students studying physics (65) and the total number of students studying chemistry (40).

2. Next, we need to find the intersection or the overlapping area between the two sets. In this case, the overlapping area represents the number of students studying both physics and chemistry.

3. To find the intersection, we subtract the total number of students studying physics (65) minus the number of students studying physics only.

4. Similarly, to find the intersection, we subtract the total number of students studying chemistry (40) minus the number of students studying chemistry only.

So, the equation becomes:

Intersection = Number of students studying physics - Number of students studying physics only
= 65 - (Total number of students - Number of students studying physics)

and

Intersection = Number of students studying chemistry - Number of students studying chemistry only
= 40 - (Total number of students - Number of students studying chemistry)

5. After substituting the given values, we have:

Intersection = 65 - (93 - 65)
Intersection = 65 - (93 - 65)
Intersection = 65 - 28
Intersection = 37

Therefore, 37 students study both physics and chemistry.