Let D be the set of digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9). Define a relation R on the power set P(D) by A R B if Card(A) = Card (B). a. Show that R is an equivalence relation. b. List the elements in the equivalence class [Ø] and in [D]. c. List the elements in the equivalence class [{4}]. d. Describe the elements in the equivalence class [{4,7}].

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Q: How many equivalence relations on the set {1, 2, 3}?

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A: Step 1: First find out the (m,n) which belong to the equivalence classes R for x, y ∈ A. As mRn ⟺…

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A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

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Q: Give an example of an equivalence relation R on the set Q such that there are exactly three distinct…

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A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

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Q: 6. (a, b), C

A: Let R be the relation on the set of ordered pairs of positive integers such that a,b,c,d∈R if and…

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