Question: Let A be a set and I an index set where, for each i I, Ri is a relation on A. Prove or disprove each

Let A be a set and I an index set where, for each i ˆˆ I, Ri is a relation on A. Prove or disprove each of the following.
(a)

is reflexive on A if and only if each Ri is reflexive on A.
(b)

is reflexive on A if and only if each Ri is reflexive on A.

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a False Let A 1 2 I l 2 R 1 1 1 R 2 2 2 Then i I R i is reflexive but neither R 1 nor R 2 is reflexive Conversely however if R i is reflexive for all actually at least one i I then i I R i is reflexive b ... View full answer

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