Question

C₁= 5

C₂= 6

A1 Rewrite the following sentence using variables and logical or mathematical symbols. Limit yourself to as few English words as possible, but it must be an equivalent statement. "e to the power of some integer times the square root of minus 1 is a complex number that is not real”. A2 Let S := {kt, ..., kg;} be a set of containing certain possibly equal complex numbers, and let T be the set of integers lying between (and perhaps equal to) Ci 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

9:5, C₂ = 6 kel w SPK K22 = { ki, K₂, kq, ky, ks } To 5,63 C = SXT a) e- Set - Roster notation of c SXT CECK,,5), (K2,5) ---, (K5,5), (196) , (Kq2b), (K5, 6} 9 b) set-builder Notation Czy 19, b) : a es' and bet c) Cardinality of C icli | SXTU = 151X ITI s has 5 members and I has 2 members 50, C has 5X2 2 3 cardinality of C is 10 d. if c has a subset Cardinality 5, say H. Then there is no condition on s Mather than first element of members of H is of S. -10 members that CS Scanned with CamScanner

For example = { Kg K2, K3, kq , Kg} of a is from ' any member ca, b) EH then s and b from T. can be AL; 1? the e to power of some integer times the square root minus I is a complex that not real" number of minus is Mathematically, enchi) in = e ne Integers 0 is a complex number which is not real. CS Scanned with CamScanner