6.8.31 Set theory

Condition: For a given set-theoretic identity: a) illustrate the identity with an Euler-Venn diagram; b) check the identity using the method of characteristic functions. \[ (A \cup B) \triangle(A \cup C)=\bar{A} \cap((B \cap \bar{C}) \cup(\bar{B} \cap C)) \text {. } \]