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## Homework Statement

The set A has 5 elements.

1. How many relations exist on A?

2. How many of those relations are symmetric and reflexive?

## The Attempt at a Solution

Some of the parts of this question are harder than others.

1. By simple counting, there are 2^(5^2) or 2^25 total relations. Some 33 million

2. This is the one I'm having the most trouble with, and I think its a confusion with definition.

A relation is symmetric if it maps an element back onto itself. Since there are 5 elements, there are 2^5 relations, just by this consideration, which are reflexive. They are also symmetric, by virtue of mapping only onto themselves.

My question is, is a relation still considered reflexive if it maps onto itself AND another element? For example, if I index the elements of A 1 through 5, is:

R = {(1,1), (5,5), (1,5), (5,1)} a reflexive relation?