Case study·Hard exam skill (4/5)·No calculatorNeeds mentor review

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

In a school activity, A={1,2,3,4,5}A=\{1,2,3,4,5\} represents five students. Students 1,3,51,3,5 are in one house and students 2,42,4 are in another house. Define aRbaRb if students aa and bb are in the same house.
Total: 4 marks

(a) State whether 1R31R3 and 1R21R2 are true. (1 mark)

(b) Find the equivalence class [4][4]. (1 mark)

(c) Check whether RR is reflexive, symmetric, and transitive. (2 marks)

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cbse-math-12.u1.t1-1.case.005

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