Prob. Let A,B,C be any three sets, then prove that-

Prob. Prove that-

Prob. If A, B, C, D are any four sets then prove that -

Prob. Show that-

(P∩Q)X(R∩S) = (PXR)∩(QXS)

Prob. Show that the relation-

R = {(a,b)| a, b ∈ Z and a - b is divisible by 3}

Is an equivalence relation, where Z is the set of all integers.

Prob. Let R be a binary relation on the set of all integers such that R= {(a, b)|(a - b ) is an even integer}. Is R an equivalence relation?

Prob. Let R be the relation defined on the integers by aRb if a - b is even. Show that R is an equivalence relation.

Prob. Let R be a binary relation on the set of all positive integers such that

R = {(a, b): | a - b | ≤ 1, a, b, are positive integers}.

Is R an equivalence relation ?

**Discrete Structure**

**EasyExamNotes.com covered following topics in these notes.**

- SET
- Mathematical Induction
- Relation
- Binary operations
- Algebraic struture
- Group
- Numerical problems on GROUP
- Subgroup
- Abelian Group or Commutative group
- Coset
- Factor or Quotient group
- Cyclic group
- Ring
- Numerical problems on RING
- Field
- POSET, Hasse diagram,Upper and Lower Bounds
- Hasse diagram
- Upper and Lower Bounds
- Lattice
- Recurrence relation numerical problems
- How to solve generating function

**A list of Video lectures**

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