W2012 - mt 1 - 9 February 2012 Name 50 minutes Student No 62-190-02 Mathematical Foundations Test 1 Solutions Write only on these pages There is an

# W2012 - mt 1 - 9 February 2012 Name 50 minutes Student No...

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9 February 2012 Name 50 minutes Student No. 62-190-02 — Mathematical Foundations – Test 1— Solutions Write only on these pages. There is an extra page at the end, if you need the space. As well as the axioms, you may use any theorem proved in class. 1 . / 10 2 . / 10 3 . / 10 4 . / 10 5 . / 5 Page 1 of 7
62– 190–02 Test 1 W2012 1.(a) LetAbe a subset ofR. Write the symbolic form of the statementAhas no largest element”.Soln.¬(xA,yA, yx).xA,yA, y > x.(b) LetAbe the interval [0, π). Prove thatAhas no largest element. Page 2 of 7
62– 190–02 Test 1 W2012 2.(a) Complete the following definition:Forx, yZ,xdividesymeans . . .kZ, y=kx.(b) Prove, for allnN, ifndivides 3, thenn= 1 orn= 3Proof.