= 1. Suppose RCQ x Q is a relation on a set Q. In the videos,...

 

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= 1. Suppose RCQ x Q is a relation on a set Q. In the videos, we defined its equivalence closure as follows. First, we take the reflexive symmetric closure of R. which is Ro AQURUR, where Ao is the diagonal relation on Q and R is R's converse relation. Then define Rn+1 = Rn; R for all n E N where; is the relational composition operation. (Note, this means R₁ = Ro: Ro, and R₂ = R₁; Ro= (Ro: Ro); Ro, etc.) 00 Then the equivalence closure of R is e(R) = R₁, Prove that the equivalence closure of a relation is an 11=0 equivalence relation. = 1. Suppose RCQ x Q is a relation on a set Q. In the videos, we defined its equivalence closure as follows. First, we take the reflexive symmetric closure of R. which is Ro AQURUR, where Ao is the diagonal relation on Q and R is R's converse relation. Then define Rn+1 = Rn; R for all n E N where; is the relational composition operation. (Note, this means R₁ = Ro: Ro, and R₂ = R₁; Ro= (Ro: Ro); Ro, etc.) 00 Then the equivalence closure of R is e(R) = R₁, Prove that the equivalence closure of a relation is an 11=0 equivalence relation.

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Answer Given Rn1 Rn R1 R0 R2R1 Equivalence relation of R eR Closure of equiva... View the full answer