What is a statement that is always true, whatever you insert, called?
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Tautology
“A or not A” is always true.
💡 Did you know? Its opposite is a contradiction.
12 questions · Maths & Logic
Logic is the art of clean thinking: it ensures that true premises lead to true conclusions, and it lies wherever precise reasoning is needed: from the mathematical proof to the computer program to the puzzle book on the kitchen table. Knowing its building blocks lets you see through arguments and tricky tasks far faster. This pack explains the most important terms and puzzle types: recognise the always-true tautology and the always-false contradiction, the conjunction as logical AND and the disjunction as logical OR, negation as denial and implication as the if-then link, the universal quantifier as a statement about all things and the existential quantifier as a statement about at least one thing, complete induction and proof by contradiction as classic methods of proof, as well as the popular logic puzzles Sudoku and the crossword: recognise them by their meaning and sharpen your own mind along the way. For logic is not just for mathematicians: it helps anywhere you need to tell good arguments from bad and make clear decisions.
Practise for freePurFact brings every card back right before you would forget it. That's how knowledge sticks.
Tautology
“A or not A” is always true.
💡 Did you know? Its opposite is a contradiction.
Contradiction
“A and not A” is always false.
💡 Did you know? Proofs use it deliberately (proof by contradiction).
Conjunction
It is true only if both parts are true.
💡 Did you know? Symbol: ∧.
Disjunction
It is true if at least one part is true.
💡 Did you know? Symbol: ∨.
Negation
It turns true into false and vice versa.
💡 Did you know? Symbol: ¬.
Implication
From a false premise anything follows.
💡 Did you know? Symbol: →.
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