My Math Forum Truth Table,validity...

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 February 18th, 2012, 09:00 PM #1 Newbie   Joined: Jan 2012 From: France Posts: 22 Thanks: 0 Truth Table,validity... Hi, I need to show that $A \rightarrow B;$ $therefore$ $A \rightarrow (B \vee C)$ is a valid argument. I used a truth table, and it worked, but i'm actually required to use an "informal proof" which means to use words, and to be precise. Anyone would know how I could actually explain it? Thank you, Jonathan
February 19th, 2012, 08:06 AM   #2
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Re: Truth Table,validity...

Hello, john616!

Quote:
 $\text{I need to show that: }\A \to B)\;\Longrightarrow\;\big[A \to (B\,\vee\,C)\big]\,\text{ is a valid argument.}" /> I used a truth table, and it worked, but i'm actually required to use an "informal proof" [color=beige]. . [/color]which means to use words, and to be precise. Anyone would know how I could actually explain it?

$\text{W\!e have: }\:A\to B \;\equiv\; \sim\!A\,\vee\,B\,\text{ is true.}$

$\text{Then }\,(\sim\!A\,\vee\,B)\,\vee\,C\,\text{ is true, regardless of the truth-value of }C.$

$\text{Therefore: }\\sim\!A\,\vee\,B)\,\vee\,C \;\equiv\;\sim\!A\,\vee\,(B\,\vee\,C) \;\equiv\;A \to (B\,\vee\,C)" />

[color=beige]. . [/color]$\text{I'll let }you\text{ supply the reasons.}$

 February 19th, 2012, 12:33 PM #3 Newbie   Joined: Jan 2012 From: France Posts: 22 Thanks: 0 Re: Truth Table,validity... $Thank$ $You$ $so$ $much$ $Soroban$ $!!$

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