Question

1. Sean A = {a, b} , B = { 2,3} , C = { 3, 4}
Hallar: a) A x (B∪ C)
b) (A x B) ∪ (A x C)
c) A x (B ∩ C)
d) (A x B) ∩ (A x C)

Answer 1

Respuesta:

Explicación paso a paso:

$\texttt{Sean}\\A=\{a,b\}\,\,,B=\{2,3\}\,\,,C=\{3,4\}\\\texttt{Hallar:}\\\\A\times(B\cup C)\\(A\times B)\cup(A\times C)\\A\times(B\cap C)\\(A\times B)\cap(A\times C)\\\texttt{SOLUCI\'ON}\\B\cup C=\{2,3,4\}\\A\times(B\cap C)=\{a,b\}\times\{2,3,4\}=\{a2,a3,a4,b2,b3,b4\}\\A\times B=\{a,b\}\times\{2,3\}=\{a2,a3,b2,b3\}\\A\times C=\{a,b\}\times\{3,4\}=\{a3,a4,b3,b4\}\\(A\times B)\cup(A\times C)=\{a2,a3,b2,b3\}\cup\{a3,a4,b3,b4\}=\{a2,a3,a4,b2,b3,b4\}\\B\cap C=\{2,3\}\cap\{3,4\}=\{3\}\\A\times(B\cap C)=\{a,b\}\times\{3\}=\{a3,b3\}\\A\times B=\{a2,a3,b2,b3\}\\A\times C=\{a3,a4,b3,b4\}\\(A\times B)\cap (A\times C)=\{a3,b3\}$

Saludos