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DUCCL Copy 1 Normal ter B 1 U - ebe X, X Amy. A. - EEEE DED... Format Painter board Font Paragraph Laat 1 1 1 2 A = 101 1210 (a) Bepaal A (a) Find A Question 5 Let A = {1, 2, 3) and B = {4,5). (a) List the elements in Ax B. 112111 211... A = 101101 = .. 1 2 1 0] [210] [... (b) On how many ways can pairs of two different letters in any order be chosen from AU B? (b) Laat G 'n grafiek wees met hoekpunte (punte) en en laat A sy aangrensendematriks wees. Gebruik die antwoord in deel () om die aantal lynrye van lengte 2 vanaf ty na ty te vind. Moenie G teken om hierdie probleem op te los nie. (b) Let G be a graph with vertices 01, 2 and Vy and let A be its adjacency matrix. Use the answer to part (a) to find the num- ber of walks of length 2 from u to vy. Do not draw G to solve this problem. (c) Write down the 8 subsets of A. (d) How many subsets has AU B? (f) Let A be the event described in (e) and B the event that the letters C,O and M remain in this order directly next to each other. What is the probability that A and B will happen together? (e) On how many ways can the order of the letters in the word COMPUTERS be changed in such a way that the let- ters P,UT,E, and R remain in this order directly next to each other? O words CE English (United States) Type here to search

PER TU hs Select Adobe PDF Adobe Ad Styles 5 Editing symbols meaning true (T), false (F), incomplete (1) VER, P(3) for all elements in the set R &A I is not an element of A А С В A is an element of B A&B A = {x,y,a,b} set A contains the elements z, {x,y} and {(a,b)} the two ordered pairs are equal ((-2), - 22) = (4, - 4) the two ordered pairs are equal ( +) = (2,-2) E.(-2)) = (3. - 8) the two ordered pairs are equal P...9 p="40 is big", o = "40 is less than 41", 40 is big but smaller than 41 if p then q and if q then p -9 p p only if a - p=q P Z → B, В ..2 Z = 'Zet is dishonest, B = 'Zet sits at the back', if Zet is dishonest then Zet sits at the back, Zet sits at the back, therefore Zet is dishonest Z = 'Zet is dishonest', B = "Zet sits at the back, if Zet is dishonest then Zet sits at the back, Zet does not sit at the back, therefore 2 "В B, T P(AUB) = T If A and B are any events in the sample space S then the probability of the union of the two events A and B equals the probability of A plus the probability of B DM

(c) Indicate the set (AUB) n (An B) on the Venn diagram below and explain the similarities between it and the logical equivalences in (b). (An B) is the complement of An B. here to search

Vraag 3 - - Question 3 (a) Gebruik die waarheidstabel hieronder (a) Use the truth table below to prove that om te bewys dat die argument a Ap, bAp. the argument a Ap, b Ap, .. (a Ap) + bp, geldig is. In elkeen .:: -( a p ) → b p, is valid. In each van die kritieke rye omkring die hipoteses of the critical lines encircle the hypotheses (aannames) en die gevolgtrekking wat waar (assumptions) and the conclusion that are true. a b p (anp) anp bap (ap) +bp Τ Τ Τ TTF IT F TI I I FI T F F F T T F T F F F T T F | F F F T I EEEEEEE (b) Gebruik o.a. die algemene resultaat a + b = na Vb om wiskundig, sonder 'n waarheidstabel, te bewys dat (b) Use the general result a + b = navb amongst others to prove mathematically, without a truth table, that (p+) = "p19.

Answer 1

Question ③ *={1,2,3} -24,58 IS A x B= {0,4), (1,5), (2,4), (2,5), (3,4), (4,5)} or AXB = 3 cab) | aca be BS AUB= {1,2,3,4,5} to choose pair of two diffrent letters / numbers we can choose ar (1,2), (1,3), (1,4), (1,5), (2,3),(2,5),(2;5). (3,4), (3,5),(4,5), (2,1), (3,1), (4,1), (5.1) (3,2), (4,2), (5,2), (4,3), (5,3), which are 20 it order matters coder does not (which matter are firar thert to sucs to elements in elements the list.) - A ito {1,2,34 poner set (ie. Set of all subsets of A) Contain 238 elements 26. {1}, { 27, 238, {1,25 4,8), 22,35, 21,2,358 & AUB={1,2,3,4,54 AUBI = S . AUR har 25 = 82 Subsets. (all subsets = candinality of power set of AUB)