Question

A2 Let S := {k1, ..., kc,} be a set of containing certain possibly equal complex numbers, and let T be the set of integers lying between (and perhaps equal to) C1 and C2. Let C be the Cartesian product of S and T. a. Write C using set-roster notation. b. Write C using set-builder notation. c. What are the possible sizes (cardinalities) of C? d. If C has a subset of cardinality 5, what conditions on S are there? If there are no conditions say so.

Answer 1

Let sa {k,, kc,} be a set of Containing certain possibly Equal complex numbers, and let T be the set of Integers lying between C, f C₂ Cand perhops Equal to) Assume 4-5,C2=2 . 15171 f 15155 (0,=5) 4 1717,2 f 17154 .: let C = SXT - A) C={Lk,, 2) , (k212) (K3,2), (K5,2) (k1,3), (k2,3), (ks, 3) (K1,4), (K2) 4), . (ks; 4) (K, ,5),(k2,5), -.-...(K5,5) no 1 i. Here T = {2, 2,3,4,5 LWLOG Assure) &s= {k, , Kz, kz,ky,ks} (b) { ca, b) laes & bET}

2 (C) IS1 = 1,2,3,4,5 (Possible) 1T1 = 2, 3, 4 .“. ICL - IsXT = 2, 3, 4, 4, 6, 8,9,12,16,10,15,20 these are possible cordinaties Cordinaties of c (d) If c has a subset of cordinality S, then there are conditions on s :: if | S1 = 1 then max IT/P04 .: max IsxT lie max ICI - 4 -). Subset of Cordinality of s is not possible .: If IT!=2 then Isl=3 le the set s must have three distinct complex numbers so that ISXT1=6 Subset of Cordinatily 5. f IT1>2 & it have a If

3 then 151=2 Since nx 27,6 en > Z I SXTI 76 it have subset of Cordinalitys these are two Conditions are on's'.