Cho các tập hợp: \(A=\left\{a,b,c\right\}\) ; \(B=\left\{b,c,d\right\}\) ; \(C=\left\{b,c,e\right\}\). Khẳng định nào sau đây là đúng?
\(A\cup\left(B\cap C\right)=\left(A\cup B\right)\cap C\).\(A\cup\left(B\cap C\right)=\left(A\cup B\right)\cap\left(A\cup C\right)\).\(\left(A\cup B\right)\cap C=\left(A\cup B\right)\cap\left(A\cup C\right)\).\(\left(A\cup B\right)\cap C=\left(A\cup B\right)\cup C\).Hướng dẫn giải:\(A\cup\left(B\cap C\right)=\left\{a,b,c\right\}\cup\left\{b,c\right\}=\left\{a,b,c\right\}\)
\(\left(A\cup B\right)\cap\left(A\cup C\right)=\left\{a,b,c,d\right\}\cap\left\{a,b,c,e\right\}=\left\{a,b,c\right\}\)
Nên \(A\cup\left(B\cap C\right)=\left(A\cup B\right)\cap\left(A\cup C\right)\)
