Respuesta :
Answer:
(a) [tex]A\cup B=\{1,2,3,5,6,8,9,10\}[/tex]
(b) [tex]B\cap C=\{\}[/tex]
(c) [tex]A-B=\{1,5,8,10\}[/tex]
(d) [tex]B\times C=\{(2,1),(2,5),(2,7),(3,1),(3,5),(3,7),(6,1),(6,5),(6,7),(9,1),(9,5),(9,7)\}[/tex]
(e) [tex]P(C)=\{\{\},\{1\},\{5\},\{7\},\{1,5\},\{1,7\},\{5,7\},\{1,5,7\}\}[/tex]
Step-by-step explanation:
Given information:
A, B and C are three sets:
A={1,3,5,6,8,10}, B = {2,3,6,9}, C = {1,5,7}
A set contains distinct elements.
(a)
We need to find the set AUB. In this set all elements of A and B are included.
[tex]A\cup B=\{1,2,3,5,6,8,9,10\}[/tex]
(b)
We need to find the set B∩C. In this set all common elements of B and C are included.
[tex]B\cap C=\{\}[/tex]
It is an empty set because there is no common element in set B and C.
(c)
We need to find the set A-B. In this set all elements of A are included excluding the common elements of A and B.
[tex]A-B=\{1,5,8,10\}[/tex]
(d)
We need to find the set BxC.
BxC is defined as
[tex]B\times C=\{(x,y):x\in B,y\in C\}[/tex]
[tex]B\times C=\{(2,1),(2,5),(2,7),(3,1),(3,5),(3,7),(6,1),(6,5),(6,7),(9,1),(9,5),(9,7)\}[/tex]
(e)
We need to find the set P(C). It is a power set of C. It is the collection of all subsets of set C.
[tex]P(C)=\{\{\},\{1\},\{5\},\{7\},\{1,5\},\{1,7\},\{5,7\},\{1,5,7\}\}[/tex]
