MAA 3200 Midterm: MAA 3200 FIU Exam 213k
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1a) [10pts] let g : a b and f : b c. prove that if f g : a c is onto, then f is onto. 1b) [10pts] disprove the converse of the previous claim: [5pts] give an example of an anti-symmetric equivalence relation on n . 3a) [10pts] let s = n n , and de ne a relation on s by (a, b) (c, d) i ad = bc. 3b) [5pts] list three elements of [(3, 5)]: [10pts] show that (0, 1) [0, 1] (same cardinality). You may use any theorems covered in class: [10pts] state the second principle of induction (often called strong induction). 6a) [7pts] let f : r r be de ned by f (x) = x (the oor function). 7a) [5pts] de ne z/5 = {0, 1, 2, 3, 4} to be the usual congruence classes (equivalence classes) mod 5, as in ch 4. 5.
