There are 40 students in a chemistry class and 60 students in a physics class. Find the number of students, which are either in physics class or chemistry class in the following case: The two classes meet at different hours and 20 students are enrolled in both the subjects.

Question

There are 40 students in a chemistry class and 60 students in a physics class. Find the number of students, which are either in physics class or chemistry class in the following case: The two classes meet at different hours and 20 students are enrolled in both the subjects.

Vedantu Content Team · Accepted Answer

Hint:  Here, we will assume that A be the students in chemistry class, B be the students in physic class and then use the property $$n\left( {{\text{A}} \cup {\text{B}}} \right) = n\left( {\text{A}} \right) + n\left( {\text{B}} \right) - n\left( {{\text{A}} \cap {\text{B}}} \right)$$, where $$n\left( {{\text{A}} \cup {\text{B}}} \right)$$, which are either in physics class or chemistry class.Complete step-by-step answer:Let us assume that A be the students in chemistry class and B be the students in physics class.Since we are given that there are 40 students in a chemistry class, 60 students in a physics class and two classes meet at different timings then there can be 20 students in both the classes.We know the property, $$n\left( {{\text{A}} \cup {\text{B}}} \right) = n\left( {\text{A}} \right) + n\left( {\text{B}} \right) - n\left( {{\text{A}} \cap {\text{B}}} \right)$$.Finding the value of $$n\left( {\text{A}} \right)$$, $$n\left( {\text{B}} \right)$$ and $$n\left( {{\text{A}} \cap {\text{B}}} \right)$$ from the given conditions, we get$$n\left( {\text{A}} \right) = 40$$$$n\left( {\text{B}} \right) = 60$$$$n\left( {{\text{A}} \cap {\text{B}}} \right) = 20$$Substituting the above values in the above property to find the number of students, which are either in physics class or chemistry class, $$n\left( {{\text{A}} \cup {\text{B}}} \right)$$, we get$$   \Rightarrow n\left( {{\text{A}} \cup {\text{B}}} \right) = 40 + 60 - 20   \\   \Rightarrow n\left( {{\text{A}} \cup {\text{B}}} \right) = 80   \\  $$Thus, there are 80 students, which is either physics class or chemistry class.Note: In solving these types of questions, students need to know the meaning of cardinality and their properties and then this problem is very simple.