Let P S denote the power set of S = 1 , 2 , 3 , … , 10 . Define the relations R 1 and R 2 on P S as A R 1 B if A ∩ B c ∪ B ∩ A c = ϕ and A R 2 B if A ∪ B c = B ∪ A c , ∀ A , B ∈ P S . The

Question

Let P S denote the power set of S = 1 , 2 , 3 , &#8230; , 10 . Define the relations R 1 and R 2 on P S as A R 1 B if A &#8745; B c &#8746; B &#8745; A c = &#981; and A R 2 B if A &#8746; B c = B &#8746; A c , &#8704; A , B &#8712; P S . Then :

Quantrex Academy · Accepted Answer

Correct answer: A. both R 1 and R 2 are equivalence relations

Given, S = 1 , 2 , 3 , &#8230; &#8230; 10 P S = power set of S A R 1 B &#8658; A &#8745; B c &#8746; A c &#8745; B = &#981; Now for reflexive property, replacing B with A we get, A &#8745; A c &#8746; A c &#8745; A which &#981; always, Now checking symmetric we will interchange A &#160; &#38; &#160; B , So, B &#8745; A c &#8746; B c &#8745; A which is same as A &#8745; B c &#8746; A c &#8745; B , hence the relation is symmetric, So, R 1 is reflexive, symmetric Now checking for transitive A &#8745; B c &#8746; A c &

Let P S denote the power set of S = 1 , 2 , 3 , … , 10 . Define the relations R 1 and R 2 on P S as A R 1 B if A ∩ B c ∪ B ∩ A c = ϕ and A R 2 B if A ∪ B c = B ∪ A c , ∀ A , B ∈ P S . Then :

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Correct answer

Step-by-step solution

More from Sets and Relations

Let P S denote the power set of S = 1 , 2 , 3 , &#8230; , 10 . Define the relations R 1 and R 2 on P S as A R 1 B if A &#8745; B c &#8746; B &#8745; A c = &#981; and A R 2 B if A &#8746; B c = B &#8746; A c , &#8704; A , B &#8712; P S . Then :

Options

Correct answer

Step-by-step solution

More from Sets and Relations

Let P S denote the power set of S = 1 , 2 , 3 , … , 10 . Define the relations R 1 and R 2 on P S as A R 1 B if A ∩ B c ∪ B ∩ A c = ϕ and A R 2 B if A ∪ B c = B ∪ A c , ∀ A , B ∈ P S . Then :