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  3. 1. . let a = {1,2,3,4,5}, b = {1,3,5,7,9}, and c =

1. . Let A = {1,2,3,4,5}, B = {1,3,5,7,9}, and C = {2,6,10,14}. a. Compute the following...

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Advance Math

1. . Let A = {1,2,3,4,5}, B = {1,3,5,7,9}, and C ={2,6,10,14}.

a. Compute the following sets: A?B, A?B, B?C, B?C, AB, BA.

b. Compute the following sets: A?(B?C), (A?B)?(A?C), A?(B?C),(A?B)?(A?C).

c. Prove that A?B = (AB)?(A?B)?(BA).

2. Let C0 = {3n : n ? Z} = {...,?9,?6,?3,0,3,6,9,...} C1 = {3n+1: n ? Z} = {...,?8,?5,?2,1,4,7,10,...} C2 = {3n+2 : n ? Z} ={...,?7,?4,?1,2,5,8,11,...}.

a. Prove that the sets C0, C1, and C2 are pairwise disjoint.

b. Compute C0 ?C1 ?C2.

3. Let R>0 be the set of positive real numbers, that is,R>0 = {x ? R : x > 0}.

Prove that {e x : x ? R} = R>0 and {logx : x ? R>0} =R.

Answer & Explanation Solved by verified expert
3.9 Ratings (709 Votes)
1 Given sets are A 12345 B 13579 C 261014a We will find We know that A union B is a set containing all the elementspresent in set A or set B So A intersection B is a set containing all the elementspresent in    See Answer
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