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Show that R is a partially ordering relation.

For a given set A, consider the relation R={(x,y)|x∊P(A), y∊P(A) and x≤y. Show that R is a partially ordering relation.

Proof: For all a∊P(A), a≤a

⟹(a,a) ∊R, R is reflexive

Let (a,b) ∊R and (b,a) ∊R then a≤b and b≤a implies that a=b.

∴ R is an anti-symmetric.

Let (a,b) ∊R and (b,c) ∊R then a≤b and b≤c, implies that a≤c i.e.,(a,c) ∊R.

∴ R is a partially ordering relation.(Proved)

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