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**1. Let R be a relation on X that satisfies**

a) for all a in X, (a,a) is in R

b) for a,b,c in X, if (a,b) and (b,c) in R, then (c,a) in R.

Show that R is an equivalence relation.

a) for all a in X, (a,a) is in R

b) for a,b,c in X, if (a,b) and (b,c) in R, then (c,a) in R.

Show that R is an equivalence relation.

**2. In order for R to be an equivalence relation, the following must be true:**

1) for all a in X, (a,a) is in R

2) for a,b in X, if (a,b) is in R, then (b,a) is also in R

3) for a,b,c in X, if (a,b) and (b,c) is in R, then (a,c) is in R.

1) for all a in X, (a,a) is in R

2) for a,b in X, if (a,b) is in R, then (b,a) is also in R

3) for a,b,c in X, if (a,b) and (b,c) is in R, then (a,c) is in R.

**3. The first part is given by the definition of an equivalence relation. I'm stuck on proving part b. Help please!**