To show that is reflexive, you need to show that
This clearly follows from the fact that are reflexive.
You're not following the definition! A relation is symmetric if .Second we need to test the Symmetric property: Let A such that and A such that . Clearly if then . Also if then , . This proves that is Symmetric.
Here, in order to show that is symmetric, you need to show
This, again, easily follows from your relations being symmetric.
Same reasoning. Here, you need to show that .Third we need to test the Transitive property: Let A such that and A such that . Clearly if then . Similarly if then . Therefore is Transitive. Since is Reflexive, Symmetric, and Transitive, it is an equivalence relation on A.
Now try proving these conditions again (you'll find something is missing for transitiveness...)
Once you've done that, b) will be much easier.
b) Is an equivalence relation on A? Prove or disprove. Suppose such that and . Then clearly . Since is not Reflexive, it is not an equivalence relation on A.