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

Question

Quizplus · Accepted Answer

The expression on the left side, $(\mathrm{A} \cup \mathrm{B}) \cap \mathrm{C}$, represents the set of elements that are in either A or B and also in C. The expression on the right side, $\mathrm{A} \cup(\mathrm{B} \cap \mathrm{C})$, represents the set of elements that are in A or in both B and C. These two expressions are not equivalent in general.

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

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