Let ~, be defined so that a,b exactly when a b is divisible by 3. Is...

 

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Let ~, be defined so that a,b exactly when a b is divisible by 3. Is this an equivalence relation? If so, list the equivalence classes. If not, which of the three properties (reflexive, symmetric, transitive) does not hold. Let2 be defined so that a~₂b exactly when a + b is even. Is this an equivalence relation? If so, list the equivalence classes. If not, which of the three properties (reflexive, symmetric, transitive) does not hold. Let ~, be defined so that a,b exactly when a b is divisible by 3. Is this an equivalence relation? If so, list the equivalence classes. If not, which of the three properties (reflexive, symmetric, transitive) does not hold. Let2 be defined so that a~₂b exactly when a + b is even. Is this an equivalence relation? If so, list the equivalence classes. If not, which of the three properties (reflexive, symmetric, transitive) does not hold.