MHB Validating Statement Using Truth Tables: Failed Basket-Weaving 101

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The discussion centers on validating a logical statement using truth tables related to studying and failing a course. The argument presented is that if studying prevents failure, and not playing cards leads to studying, then failing indicates excessive card playing. Participants suggest constructing a truth table to analyze the implications of the statements involved. Recommendations include breaking down the statements into simpler propositions and using mnemonic names for clarity. The conversation emphasizes the importance of logical reasoning in validating the argument.
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If I study, then I will not fail basket-weaving 101. If I do not play cards to often, then
I will study. I failed basket-weaving 101. Therefore, I played cards too often. Is this
statement valid (use truth tables to verify).
 
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trevor said:
If I study, then I will not fail basket-weaving 101. If I do not play cards to often, then
I will study. I failed basket-weaving 101. Therefore, I played cards too often. Is this
statement valid (use truth tables to verify).

Have you constructed a truth table? Care to share? :). If not, I recommend breaking down all the words into a string of implications. For example, let A be the statement "I study", B be the statement "I failed basket-weaving" etc and use these to help with the truth table.
 
Joppy said:
Have you constructed a truth table? Care to share? :). If not, I recommend breaking down all the words into a string of implications. For example, let A be the statement "I study", B be the statement "I failed basket-weaving" etc and use these to help with the truth table.

Thank you. I will send what I find
 
I would also recommend using mnemonic names for propositions, such as $S$ for "I studied" and $F$ for "I failed basket-weaving".
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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