25 topics
Logic and reasoning help, from truth tables to fallacies
Logic grades the shape of an argument, not whether you agree with where it lands. An argument can be flawless and still reach a false conclusion, and a conclusion you know is true is no evidence at all that the reasoning behind it was any good. Getting comfortable with that split is most of the course, and it is why an answer that feels obviously right can still be worth zero.
Where students get stuck
Valid, sound, true — I use these words interchangeably and lose marks
They describe different things and the marker is checking that you know which is which. Truth is a property of one statement. Validity is a property of the structure of an argument: if the premises were true, the conclusion would have no way to escape. Soundness is both at once, valid and with premises that happen to be true. So all cats are green, Fluffy is a cat, therefore Fluffy is green is perfectly valid and not remotely sound. Testing validity means deliberately setting aside whether the premises are true and asking only whether the conclusion is forced.
Converse, inverse, contrapositive — which one is the equivalent again?
Only the contrapositive. Take if it rains, the game is cancelled. The converse swaps the halves: if the game was cancelled then it rained, which does not follow, because it could be cancelled for any number of reasons. The inverse negates both halves without swapping: if it does not rain the game is not cancelled, the same error wearing a different coat. The contrapositive both swaps and negates: if the game was not cancelled then it did not rain, and that is guaranteed. Read a conditional as a promise, and the contrapositive is simply that promise restated.
Negating a sentence with all or some comes out backwards
Negation flips the quantifier and then negates what follows it. The opposite of all swans are white is not no swans are white — it is at least one swan is not white, which is why a single counterexample destroys a universal claim while a single example never proves one. The opposite of some student failed is every student passed. With two quantifiers, flip them one at a time from left to right: the negation of for every x there is a y such that P is there is an x such that for every y, not P. Working left to right in order is what keeps the sentence from coming out reversed.
Affirming the consequent looks perfectly fine to me
It looks fine because the conclusion is often true anyway, and that is precisely the trap. From if it rains the ground is wet, plus the ground is wet, you cannot conclude it rained — a sprinkler produces the same evidence. The conditional only licenses two moves: affirm the antecedent to get the consequent, or deny the consequent to deny the antecedent. Denying the antecedent fails for the same reason, since no rain does not guarantee dry ground. The reliable test is to keep the shape and swap in content where you can see the conclusion is false.
What's covered
Logic & Reasoning topics you can work through with a tutor, generate practice on, or turn into flashcards and a study plan.
Arguments
- Premises, conclusions and indicator words
- Deductive versus inductive reasoning
- Validity, soundness and inductive strength
- Putting an argument into standard form
- Hidden premises and charitable reading
Propositional logic
- Statements, connectives and symbolisation
- Truth tables
- Logical equivalence, tautology and contradiction
- Conditionals, converse, inverse and contrapositive
- Rules of inference and natural deduction
Predicate logic
- Universal and existential quantifiers
- Symbolising English sentences
- Negating quantified statements
- Nested quantifiers
- Counterexamples and models
Fallacies and bias
- Affirming the consequent and denying the antecedent
- Straw man, ad hominem and false dilemma
- Slippery slope and appeal to authority
- Correlation mistaken for causation
- Cognitive bias and motivated reasoning
Reasoning in practice
- Weighing evidence and evaluating sources
- Analytical reasoning puzzles
- Logical reasoning questions on admissions tests
- Syllogisms and Venn diagram testing
- Structuring an argument in an essay
Logic & Reasoning questions
Is this for a philosophy logic course or the logic unit in math and computer science?
The list covers both, and they overlap more than students expect. Philosophy courses spend longer on argument reconstruction and fallacies; math and computer science courses push further into symbolisation, formal proof and quantifiers. Tell it which department is marking you and it will use that notation.
I have a take-home logic quiz tonight. Will it answer it for me?
It will not fill in your quiz. It will build a parallel question with the same structure, work that one through with you, then hand yours back for you to attempt. Logic is one of the few subjects where doing three problems yourself genuinely does fix the fourth.
Can it check whether the argument in an article I have been assigned holds up?
Yes. Share the screen or read it aloud and it will pull out the premises, name what is being assumed but never stated, and point to where the inference is doing work it has not earned. That is the same skill your response paper is graded on, so it is worth doing together rather than being handed a verdict.
Can it drill me on the fallacies before a test?
Flashcards handle the names and definitions, and the arcade games turn them into rapid identification, which is what a multiple-choice section is really testing. You can also ask for practice passages where the task is to spot which move in the argument is the bad one.
Stuck on logic & reasoning right now?
Talk it through out loud, share your screen, and watch it worked out step by step on a whiteboard.
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