Is this an equivalence relation

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1. Let ∼ be defined so that a ∼ b exactly when a · b is divisible by 3. Is this an equivalence relation? If not, which of the three properties (reflexive, symmetric, transitive) does not hold?

2. Encrypt the message we are all made of stars using the atbash cipher.

3. Prove that a ≡ b (mod n) if and only if n|(a - b); that is, check that the condition given in Definition 5.3.1 is correct.

Reference no: EM131239987

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