# Compound Proposition Simplification

#### steenis

##### Well-known member
MHB Math Helper
You know that $a \to b$ is equivalent to $\neg a \vee b$

Therefore $[(p \vee q) \wedge \neg p] \to q$ is equivalent to $\neg [(p \vee q) \wedge \neg p] \vee q$

Now you can simplify the last expression.

#### User40405

##### New member
You know that $a \to b$ is equivalent to $\neg a \vee b$

Therefore $[(p \vee q) \wedge \neg p] \to q$ is equivalent to $\neg [(p \vee q) \wedge \neg p] \vee q$

Now you can simplify the last expression.
Thank you so so much!

I have been checking guides the entire day and yesterday. I can now get to where you got with it, but I cannot simplify the last expression (pvq). I do not know how to change this and get the simplified form.

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Because (pvq) is equivalent to (qvp). But how does that help me?

#### Olinguito

##### Well-known member
Or use the distributive law in the first block:
$$(p\vee q)\wedge\neg p\ \equiv\ (p\wedge\neg p)\vee(q\wedge\neg p)\ \equiv\ q\wedge\neg p.$$

#### steenis

##### Well-known member
MHB Math Helper
I. study the theory

II. use $\neg (a \wedge b)$ is equivalent with $\neg a \vee \neg b$