Monomath – CBSE | GSEB | IB | JEE Maths by Ajay Yadav (Math King of Katargam) – 15+ Years Experience. Study Notes, Video Lessons, Formula Sheets & PYQs.
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Relations and Functions

Previous Year Questions (2022-2024)

📅 Year 2022

  1. Check if f(x) = x2 is injective and surjective for f: R -> R.
    Show Solution
    Not injective: f(1)=1, f(-1)=1\nNot surjective: no x gives f(x)<0\nf is neither injective nor surjective.
  2. Prove that R = {(a,b): a-b is divisible by 3} on Z is an equivalence relation.
    Show Solution
    Reflexive: a-a=0 divisible by 3.\nSymmetric: if a-b divisible by 3 then b-a also divisible by 3.\nTransitive: a-b=3k, b-c=3m => a-c=3(k+m) divisible by 3.\nHence equivalence relation.

📅 Year 2023

  1. Check if f(x) = x2 is injective and surjective for f: R -> R.
    Show Solution
    Not injective: f(1)=1, f(-1)=1\nNot surjective: no x gives f(x)<0\nf is neither injective nor surjective.
  2. Prove that R = {(a,b): a-b is divisible by 3} on Z is an equivalence relation.
    Show Solution
    Reflexive: a-a=0 divisible by 3.\nSymmetric: if a-b divisible by 3 then b-a also divisible by 3.\nTransitive: a-b=3k, b-c=3m => a-c=3(k+m) divisible by 3.\nHence equivalence relation.

📅 Year 2024

  1. Check if f(x) = x2 is injective and surjective for f: R -> R.
    Show Solution
    Not injective: f(1)=1, f(-1)=1\nNot surjective: no x gives f(x)<0\nf is neither injective nor surjective.
  2. Prove that R = {(a,b): a-b is divisible by 3} on Z is an equivalence relation.
    Show Solution
    Reflexive: a-a=0 divisible by 3.\nSymmetric: if a-b divisible by 3 then b-a also divisible by 3.\nTransitive: a-b=3k, b-c=3m => a-c=3(k+m) divisible by 3.\nHence equivalence relation.