How to Prove this WFF

**parkhid** · February 27th 2010, 04:54 AM

Hi Help To Prove this :

$ p \Leftrightarrow q \equiv (\sim p) \Leftrightarrow (\sim q) $

I Have tried this out :

$ p \Leftrightarrow q \equiv (p \Rightarrow q) \wedge (q \Rightarrow p) $

**Prove It** · February 27th 2010, 05:02 AM

Originally Posted by parkhid

Hi Help To Prove this :

$ p \Leftrightarrow q \equiv (\sim p) \Leftrightarrow (\sim q) $

I Have tried this out :

$ p \Leftrightarrow q \equiv (p \Rightarrow q) \wedge (q \Rightarrow p) $

$p \Leftrightarrow q$ means $p \Rightarrow q$ and $q \Rightarrow p$ .

From the contrapositive:

If $p \Rightarrow q$ then $(\sim q) \Rightarrow (\sim p)$ .

If $q \Rightarrow p$ then $\sim p \Rightarrow (\sim q)$ .

Therefore $p \Leftrightarrow q \equiv (\sim p) \Leftrightarrow (\sim q)$ .

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