Question

Let S be any non-empty set and P(s) be its power set. We define a relation R on P(s) by A R B to mean
A ⊆ B i.e. R = {(A,B) : A ⊆ B} then R is
1. Equivalence
2. Reflexive, symmetric but not transitive
3. Symmetric, transitive but not reflexive
4. Reflexive, transitive but not symmetric

Answer 1

Correct Answer - Option 4 : Reflexive, transitive but not symmetric

∴ A ⊆ A ⇒ A R A, ∀ A ∈ P(s)

⇒ R is reflexive

Symmetric : lefer A R B ⇒ A ⊆ B                       B ⊆ A

but not necessary so not symmetric

transitive A R B and B R C ⇒ A ⊆ B and B ⊆ C ⇒ A ⊆ C ⇒ R is transitive