Cho A = {a; b; c}; B = {b; c; d}; C = {a; b; c; d; e}. Khẳng định nào sau đây sai

Cho A = {a; b; c}; B = {b; c; d}; C = {a; b; c; d; e}. Khẳng định nào sau đây sai

A. $\left( {{\rm{A}} \cup {\rm{B}}} \right) \cap {\rm{C}} = \left( {{\rm{A}} \cap {\rm{B}}} \right) \cup {\rm{C}}$;

B. ${\rm{A}} \cup \left( {{\rm{B}} \cap {\rm{C}}} \right) = \left( {{\rm{A}} \cup {\rm{B}}} \right) \cap \left( {{\rm{A}} \cup {\rm{C}}} \right)$;

C. ${\rm{A}} \cup {\rm{(B}} \cap {\rm{C)}}\,{\rm{ = }}\,({\rm{A}} \cup {\rm{B)}} \cap {\rm{C}}$;

D. ${\rm{(A}} \cup {\rm{B)}} \cap {\rm{C}}\,{\rm{ = }}\,{\rm{(A}} \cup {\rm{B)}} \cap {\rm{(A}} \cup {\rm{C)}}$.

Đáp án đúng là: A

- Đáp án A: Ta có $A \cup B = {\rm{\{ }}a;b;c;d{\rm{\} }}$$\Rightarrow (A \cup B) \cap C = {\rm{\{ }}a;b;c;d{\rm{\} }}$

$A \cap B = {\rm{\{ }}b;c{\rm{\} }}$$\Rightarrow (A \cap B) \cup C = {\rm{\{ }}a;b;c;d;e{\rm{\} }}$

Vậy $\left( {{\rm{A}} \cup {\rm{B}}} \right) \cap {\rm{C}} \ne \left( {{\rm{A}} \cap {\rm{B}}} \right) \cup {\rm{C}}$

Đáp án A sai.

- Đáp án B: Ta có ${\rm{B}} \cap {\rm{C}} = \left\{ {{\rm{b}};c;{\rm{d}}} \right\}$ $\Rightarrow {\rm{A}} \cup \left( {{\rm{B}} \cap {\rm{C}}} \right) = \left\{ {{\rm{a}};{\rm{b}};{\rm{c}};{\rm{d}}} \right\}$;

${\rm{A}} \cup {\rm{B}} = \left\{ {{\rm{a}};{\rm{b}};{\rm{c}};{\rm{d}}} \right\}$; ${\rm{A}} \cup {\rm{C}} = \left\{ {{\rm{a}};{\rm{b}};{\rm{c}};{\rm{d}};{\rm{e}}} \right\}$ $\Rightarrow \left( {{\rm{A}} \cup {\rm{B}}} \right) \cap \left( {{\rm{A}} \cup {\rm{C}}} \right) = \left\{ {{\rm{a}};{\rm{b}};{\rm{c}};{\rm{d}}} \right\}$

Vậy ${\rm{A}} \cup \left( {{\rm{B}} \cap {\rm{C}}} \right) = \left( {{\rm{A}} \cup {\rm{B}}} \right) \cap \left( {{\rm{A}} \cup {\rm{C}}} \right)$

Đáp án B đúng.

- Đáp án C: Ta có ${\rm{B}} \cap {\rm{C}}\, = {\rm{\{ }}b;c;d{\rm{\} }}$$\Rightarrow {\rm{A}} \cup \left( {{\rm{B}} \cap {\rm{C}}} \right) = \left\{ {{\rm{a}};{\rm{b}};{\rm{c}};{\rm{d}}} \right\}$

$A \cup B = {\rm{\{ }}a;b;c;d{\rm{\} }}$$\Rightarrow ({\rm{A}} \cup B) \cap C = \left\{ {{\rm{a}};{\rm{b}};{\rm{c}};{\rm{d}}} \right\}$

Vậy ${\rm{A}} \cup {\rm{(B}} \cap {\rm{C)}}\, = \,({\rm{A}} \cup {\rm{B)}} \cap {\rm{C}}$

Đáp án C đúng.

- Đáp án D: Ta có ${\rm{A}} \cup {\rm{B = \{ }}a;b;c;d{\rm{\} }}$$\Rightarrow (A \cup B) \cap C = {\rm{\{ }}a;b;c;d{\rm{\} }}$

$\,{\rm{A}} \cup {\rm{B = \{ }}a;b;c;d{\rm{\} }}$;$\,{\rm{A}} \cup C{\rm{ = \{ }}a;b;c;d;e{\rm{\} }}$$\Rightarrow (A \cup B) \cap (A \cup C) = {\rm{\{ }}a;b;c;d{\rm{\} }}$

Vậy ${\rm{(A}} \cup {\rm{B)}} \cap {\rm{C}}\,{\rm{ = }}\,{\rm{(A}} \cup {\rm{B)}} \cap {\rm{(A}} \cup {\rm{C)}}$.