Question

Cho E={1;2;3;4;5;6} , A={3;6},B={2;3;5}

CMR :

E\(\(A\cap B\)) = (E\A)U(E\B)

E\(AUB)=(E\A)\(\cap\)(E\B)

Answer 1

+) ta có : \(A\cap B=\left\{3\right\}\) \(\Rightarrow E\backslash\left(A\cap B\right)=\left\{1;2;4;5;6\right\}\)

ta có : \(E\backslash A=\left\{1;2;4;5\right\}\) và \(E\backslash B=\left\{1;4;6\right\}\)

\(\Rightarrow\left(E\backslash A\right)\cup\left(E\backslash B\right)=\left\{1;2;4;5;6\right\}\)

\(\Rightarrow E\left(A\cap B\right)=\left(E\backslash A\right)\cup\left(E\backslash B\right)\) (đpcm)

+) ta có : \(A\cup B=\left\{2;3;5;6\right\}\) \(\Rightarrow E\backslash\left(A\cup B\right)=\left\{1;4\right\}\)

ta có : \(E\backslash A=\left\{1;2;4;5\right\}\) và \(E\backslash B=\left\{1;4;6\right\}\)

\(\Rightarrow\left(E\backslash A\right)\cap\left(E\backslash B\right)=\left\{1;4\right\}\)

\(\Rightarrow E\left(A\cup B\right)=\left(E\backslash A\right)\cap\left(E\backslash B\right)\) (đpcm)

Answer 2

Mysterious Person Akai Haruma Hung nguyen