Worksheet 1 - Selected Answers
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ntalomashele01Worksheet 1 - Selected Answers
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ntalomashele012021 WTW114 Worksheet 1 Selected answers
• Remember that in general it is not enough to simply arrive at the correct answer, you need a solid argument
to support your conclusions. So even if your final answer matches with one here, it does not necessarily mean
that you mastered the problem.
• Please make use of the padlet, discord, signal message group, tutorials and consultions to get more feedback
should you need it.
Selected answers.
9E (Did you draw a sign line?)
10C (Did you draw a sign line?)
11(a) A ∪ B = {1, 2, 3, 5, 7} (b) A ∩ B = {1} (c) (A ∪ B) ∩ C = {2, 3} (d) (A ∪ B) ∩ C = {1, 2, 3}
(e) (A ∩ B) ∩ C = ∅ (f) A ∩ (B ∩ C) = ∅ (g) A\B = {2, 3} (h) A = {1, 2, 3} (i) A ∩ ∅ = ∅
12(a),(c),(d),(e),(g),(h) is always true. The rest is not always true.
13 S = (−∞, −5] ∪ (0, 4] (Did you draw a sign line?)
√ √
14 Set of solutions: S = [−2 a, 0) ∪ [2 a, ∞)
15(a) True. First note that A\B = A\(A ∩ B) (since we can only take away elements of A that are in A). Therefore
A\B = A\(A ∩ B) = A\C.
15(b) False. Could you find a counterexample? Challenge: prove that if A\B = B\A, then A = B.
15(c) False. Did you find a counter example?
15(d) True. Could you prove it?
16 Only (e) is impossible, since if A ⊆ B, then A ∩ B = A.
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