Exam2023Proposed solution included

MATS 2101 Analysis I Exam 2023

MATS 2101: First Semester Examination 2023, University of Bamenda, Faculty of Science, Dept of Math and Comp Sc., Lecturer Prof. Shu Felix: Question 1, identifying which statements about subsets are genuine mathematical statements; Question 2, a truth table for (A⟹~B)⟺(B⟹~A); Question 3, induction proof of Bernoulli's inequality (1+x)^n≥1+nx; Question 4, partial order/equivalence/total order definitions and a worked example on a concrete relation; Question 5, injective/surjective definitions and a proof that g∘f is injective; Question 6, a Cauchy-type epsilon estimate for x_n=2/(n+2) and a limit evaluation of √(n+1)-√(n+k).

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University of Bamenda

Faculty of Science - FS

Mathematics & Computer Science - MCS

MATS21012023

Analysis I

Exam · First Semester · Level 200

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Let X and Y be sets and f : X → Y be a function. (a) When do we say that f is (i) injective (ii) surjective? (4 pts) (b) Suppose that f is as in (a) and g : Y → Z for some other set Z. Prove that if f and g are injective then g ◦ f is injective. (4 pts)

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