Question

Give a formal proof for the following tautology by using the CP rule.

(B →C) ^ A ^ B →A ^ C

Answer 1

Solution for the problem is provided below, please comment if any doubts:

Prove using conditional proof (CP) rules is following the procedure From A, derive B, then A→B.

Here A=> (B →C) ^ A ^ B

And B => A ^ C

So from A we need to derive B to prove the tautology

1. (B →C)                    :Given premise(P)
2. A                              : Given premise(P)
3. B                              : Given premise(P)
4. C                              :1, 3, Modus Ponens (MP), (B →C), B=>C
5. A^C                          :2, 4, Conjunction

QED                            :1-5 CP

Hence prove the tautology using CP rule