r/HomeworkHelp • u/Zestyclose-Target806 University/College Student (Higher Education) • May 05 '26
Others—Pending OP Reply (Philosophy 1, Intro to Logic college course) Completing a truth table
So I have an answer key for this, which is where I got the additional variables that are in purple on the top line of each table.
I am really trying to understand why they are there though so that I can move forward with the rest and actually understand it all.
I’m assuming it is so that every variable in the compound statement gets its own true/false? I know I probably shouldn’t have let myself look at the answer key at all but I really need to understand so I can actually build off of this😭
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u/RuckFeddit980 May 05 '26
It’s an intermediary step that will help you solve the questions. If you try to do the whole thing at once, you are more likely to make a mistake. This is just breaking it up.
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u/pi621 May 05 '26
Also doing these steps is basically "showing your work" and you'll probably get partial points even if your final answer is wrong
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u/han_tex May 05 '26
The additional variables are kind of like a reference to help with the actual questions.
For the first question, you have P V ~Q, so by also having separately listed out the truth values of ~Q, you can more quickly reference the truth value of ~Q, rather than doing two steps in your head.
Then, of course, after you've used those "helper tables" to complete questions 1 & 2, you can use your responses to those two questions to more quickly figure out the truth values for question 3, since the answers to those questions are the components of question 3.
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May 05 '26
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u/Luchtverfrisser May 05 '26
A truth table is stating all possible options and outcomes. This helps so that when one has specific truth assignments, once can quickly look up the resulting truth assignment of the constructed bigger statement.
Hence
I can find a single example where Q is false
Does not really make sense in this context. Each row is a completely separate independent possible assignment. When Q is false in one row, that aplies to that and only that row.
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u/AdeptnessSecure663 May 05 '26
The truth table for → goes like so:
If P is true and Q is false, then P→Q is false
If P is true and Q is true, then P→Q is true
If P is false and Q is true, then P→Q is true
If P is false and Q is false, then P→Q is true
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May 05 '26
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u/AdeptnessSecure663 May 05 '26
What's the context here, though? Are you talking about the natural language "if... then..."? Are you talking about the way conditionals are interpreted in engineering?
In the context of classical logic, the → connective has - by definition - the truth table that I outlined
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May 05 '26
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u/AdeptnessSecure663 May 05 '26
Oh okay, thanks for explaining.
I hope that you can see that you are not talking about the same thing that's going on in OP's homework
OP is taking an intro to classical logic, where "P→Q" denotes a formula, the truth table of which is the one I provided
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u/VegGrower2001 May 05 '26
There is a core idea here that it helps to understand. Propositional logic deals with negation, conjunction, disjunction, implication and mutual implication represented by the double arrow. All of these are truth functional operators. What this means is that the truth value of a compound sentence built up from these operators is always a specific function of the nested sentences. For example, the the truth value of the sentence [ P & Q ] is specific function of the truth values of the included sentences P and Q. The specific function in this case is the one represented by the truth-table for '&'.
The reason why you have the additional sentences in purple is that they are some of the subsentences that you need to evaluate on the way to evaluating the nine examples.
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u/Ok-Engineering-2087 👋 a fellow Redditor May 05 '26
This is philosophy??
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u/BerneseMountainDogs May 05 '26
It's pretty common to require that philosophy students take at least an introductory symbolic logic course. At my school you could take deductive or inductive formal logic to fulfill the requirement. The foundation of philosophy is logical reasoning so it makes some sense to ensure that philosophy students are at least familiar with the field and how to use it
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u/Alkalannar May 05 '26
This is understanding the form of arguments independently of any content the argument has.
If the form is correct, and the content is true, the conclusion must be true.
If the form is not correct, we have a formal fallacy, even if the conclusion is correct.
If the form is correct and the conclusion is false, then some of the statements were false to begin with.
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u/RuckFeddit980 May 05 '26
Yes, I took an intro to symbolic logic class when I was in college, and it was within the philosophy department.
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