# Discrete Math - Logical Equiv. & Rule of Inference

I have to use logical equivalences and rules of inference to show that p will follow from the following premises.

Given:
1. q -> p
2. m
3. (m ^ s) -> q

Show:
p


I have an idea of how I want my steps to go:

4. m ^ s    from 2     using ???
5. q        from 3,4   using Modus Ponens

p,QED       from 1,5   using Modus Ponens


I don't know if I'm heading in the right direction or not

• It doesn't necessarily follow. You need to be able to assume $s$ - otherwise $m \wedge s$ may be false, so you can't deduce $q$, so you can't deduce $p$. If $\wedge$ were $\vee$, then you'd be fine. – Patrick Stevens Oct 6 '15 at 8:46
• Would (m v s) cancel (m ^ s)? – Xirol Oct 6 '15 at 8:58
• Your first step ("4.") is false: how can you infer this? You don't have $s$ as a premise. All you can conclude from 1. - 3. is $s \rightarrow q$. – BrianO Oct 6 '15 at 11:27