Question

Let A = {a, b, c}. Then number of equivalence classes on A is:​

Answer 1

Answer: example like your question

Here,

A={1,2,3}

∴ Total possible pairs ={(1,1)(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)}

∴ Smallest equivalence relation containing (1,2),(R1)={(1,1),(2,2),(3,3),(1,2),(2,1)}

Now, if we add (2,3), then we have to add (3,2) to make it symmetric.

As (1,2),(1,3) are there, we have to add (1,3) also to make it transitive.

As we are adding (1,3), we need to add (3,1) also to make it symmetric. ∴R2={(1,1)(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)}

These are the two equivalence relations are possible.

So, B is the correct option.

Step-by-step explanation:

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Answer 2

Answer:

number of equivalence classes on A is: 8

Hope this answer helps you ^_^ !