I would use the membership table to solve the 1st problem. Set A, B and C with value 1 and 0 and you will be able to prove whether the 2 equations are logically equivalent or not. And i think it is not. Please correct me if i am wrong learning in the process.

A B C-B ^ C--A U ( B ^ C )-A U C--(A U C) ^ (A U C)

0 0 0---0---------0----------0------------0

0 0 1---0---------0----------1------------1

0 1 0---0---------0----------0------------0

0 1 1---1---------1----------1------------1

1 0 0---0---------1----------1------------1

1 0 1---0---------1----------1------------1

1 1 0---0---------1----------1------------1

1 1 1---1---------1----------1------------1