
Concept explainers
To find: Whether each relation is an equivalence relation.

Answer to Problem 30PPS
The relation is equivalence relation.
Explanation of Solution
Given information:
The given relation is “has the same birthday as”, for the set of all human being.
Calculation:
To see if this is an equivalence relation, we must check if it is reflexive transitive, and symmetric.
First check reflexive.
Does one person have the same birthday as him or herself? Yes.
Now check if it is symmetric.
If a person
Now check if it is transitive.
If person
Thus this is an equivalence relation because it is reflexive, symmetric, and transitive.
Therefore, the relation is equivalence relation.
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