If $A, B$ and $C$ are subsets of a given set, then which one of the following relations is not correct?

• Correct answer
  A

  $\mathrm{A} \cup(\mathrm{A} \cap \mathrm{B})=\mathrm{A} \cup \mathrm{B}$
• B

  $\mathrm{A} \cap(\mathrm{A} \cup \mathrm{B})=\mathrm{A}$
• C

  $(\mathrm{A} \cap \mathrm{B}) \cup \mathrm{C}=(\mathrm{A} \cup \mathrm{C}) \cap(\mathrm{B} \cup \mathrm{C})$
• D

  $(\mathrm{A} \cup \mathrm{B}) \cap \mathrm{C}=(\mathrm{A} \cap \mathrm{C}) \cup(\mathrm{B} \cap \mathrm{C})$

Solution

$A \cup(A \cap B)=A$ $\therefore$ option (a) is wrong.

Hence, the correct answer is option: 'A'.