Question

用逻辑代数的基本等价代数证明（A＋B）（B＋C）（C＋D）＝AC＋BC＋BD

Answer 1

(A＋B)(B＋C)(C＋D)

＝[(A(B＋C)＋B(B＋C)](C＋D)

=(AB＋AC＋BB＋BC)(C＋D)

=(AB＋AC＋B＋BC)(C＋D)

=(ABC＋ACC＋BC＋BCC)+(ABD＋ACD＋BD＋BCD)

=(ABC+BC+BCC+BCD)+(ACC+ACD)+(ABD+BD)

=BC+AC+BD