Question

If A = { a, b, c, d, e, f ) B-{ b, c, d, f, g) an C = {a,e,i,o,u), show that. A U (BnC) = (AUB) n (AUC)​

Answer 1

`B\cap C=\emptyset\\A\cup(B\cap C)=\{a,b,c,d,e,f\}\\A\cup B=\{a,b,c,d,e,f,g\}\\A\cup C=\{a,b,c,d,e,f,i,o,u\}\\(A \cup B)\cap (A \cup C)=\{a,b,c,d,e,f\}`

As you can see
`A\cup(B\cap C)=(A \cup B)\cap (A \cup C)`