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 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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