# MATH221 Mathematics for Computer Science | My Assignment Tutor

MATH221 Mathematics for Computer ScienceTutorial Sheet Week 8 { Autumn 20211. Let X = fa; b; c; d; e; fg. Determine whether the following statements are true or false. (i) X 2 P(X)(v) a 2 X(ii) f;g 2 P(X)(vi) X ⊆ P(X)(iii) a 2 P(X)(vii) a ⊆ P(X)(iv) fag 2 X(viii) fXg ⊆ P(X)2. Which of the following sets are equal? In some cases, you can list the elements of the sets explicitly.(i) A = f0; 1; 2g(ii) B = fx 2 R : -1 ≤ x < 3g(iii) C = fx 2 R : -1 < x < 3g (iv) D = fx 2 Z : -1 < x < 3g(v) E = fx 2 N : -1 < x < 3g3. Let U = R and let A = f1g, B = (0; 1) = fx 2 R : 0 < x < 1g and C = [0; 1] = fx 2 R : 0 ≤ x ≤ 1g. Find thesets below.A [ BA [ CA CA BB C 4. Prove or disprove the statement f0; 1g = n 2 Z : 9k 2 Z s.t. n = 1 – (2-1)k :5. Let U = N and let A = x 2 N : x is odd , B = x 2 N : x is even , and P = x 2 N : x is a prime number .Find the sets below. Are A and B disjoint? Is P ⊆ A?A P P – A B – P A – B6. Let U be the universal set and let A, B and C be subsets of U. By using the properties of f[; ; g and anyresults from lectures, simplify the following.(i)(C U) [ C (ii) (A U) [ A (iii)(C [ 😉 [ C (iv) (A B) A7. Let U be a non-empty universal set, and let A, B and C be subsets of U. Prove or disprove each of thefollowing statements.(i) A – B = B – A (ii) A – (B – C) = (A – B) – CYou may find the relation A – B = A B, the Distributive Laws and DeMorgan’s Laws helpful.

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