MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions
Problem
In a school of 180 students, each student belongs to exactly one of the four house colours: Red, Blue, Green, or Yellow. Define a relation H on the set of students by
PHQ⟺P and Q are in the same house colour.
Answer the following questions:
(i) Prove that H is an equivalence relation on the set of all students.
(ii) How many distinct equivalence classes does H produce?
(iii) If 45 students are in the Red house, determine the size of the equivalence class of any student who belongs to the Red house.