To translate truth table into English and decipher logical argument it makes

Question

This is from How to prove it by Velleman.

It will either rain or snow tomorrow.

It is too warm to snow.

Therefore, it will rain.

Let P - It will rain tomorrow, Q - It will snow tomorrow; representing the argument symbolically,

$P \vee Q$

$\neg Q$

$\therefore P$

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The last line reads as "It will rain tomorrow OR it will snow tomorrow. It will snow tomorrow. Therefore, it will rain." I did not understand it.

J. W. Perry · Accepted Answer · 2013-09-27T05:01:29.547

1

I am reading here $$(P \vee Q) \wedge \neg Q \Rightarrow P.$$

In English, "Either $P$ is true or $Q$ is true, and $Q$ is false, therefore $P$ is true." This corresponds with line 3 of your truth table. I hope that was useful in some way. Do tell if further clarification is desired.

edited Sep 27 '13 at 05:01

answered Sep 27 '13 at 02:51

J. W. Perry

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negation of Q is False, therefore Q is true – Vikram Sep 27 '13 at 04:54
I remember hearing as an undergrad of a few people missing the true/false question: $(Q \wedge\neg Q)$. Always false of course. – J. W. Perry Sep 27 '13 at 04:57
ouch!!!!!!!! I got it !!! :) thanx – Vikram Sep 27 '13 at 05:01

To translate truth table into English and decipher logical argument it makes

1 Answers1