Hi. I am reading Halmos's Naive Set Theory book. I have the following doubts.(adsbygoogle = window.adsbygoogle || []).push({});

1. In chapter 7. on relations, he says "The least exciting relation is the empty one. (To prove that ∅ is a set of ordered pairs, look for an element of ∅ that is not an ordered pair)

". Whenever someone talks about ∅ used in the context of a relation, it becomes very confusing. Formally, is there a way to logically explain as to why ∅ is a relation?

2. At the end of chapter 8., there are two excercises namely "(i) Y^{∅}has exactly one element, namely ∅, whether Y is empty or not, and (ii) if X is not empty, then ∅^{X}is empty". What do these statements mean in the first place? How do you prove them?

I have been able to understand almost everything in Halmos's book except few things which are really confusing. I kindly request you to help me understand them. I really like Halmos's style but I get struck at places and I feel very helpless during those times.

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# Empty functions and relations

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