Mathematics Homework Help

I’m working on a geometry multi-part question and need an explanation to help me learn.

• Let S be the set of fractions: S = { p/q : p , q ∈ ℤ , q≠0}( Where ℤ is the set of integers) Define a relation ~ on S by: a/b ~ c/d iff ad=bc . Is this relation an equivalence relation?
  • Is the relation reflexive? Why or why not?
  • Is the relation symmetric? Why or why not?
  • Is the relation transitive? Why or why not?
  • Is the relation an equivalence relation? Justify your answer.