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  2. human.libretexts.org › Bookshelves › Philosophy2.10: Tautologies, Contradictions, and Contingent Statements

    Apr 21, 2023 · A tautology is a statement that is true in virtue of its form. Thus, we don’t even have to know what the statement means to know that it is true. In contrast, a contradiction is a statement that is false in virtue of its form. Finally, a contingent statement is a statement whose truth depends on the way the world actually is.

  3. human.libretexts.org › Bookshelves › Philosophy33.2: Tautology, Contradiction, and Contingencies ...

    For a statement to be a contradiction, it has to always be false, so the table has to show all ‘F’s on the right side. So, if there are any ‘T’s in the table, then the statement is not a contradiction. ‘P & ~P’ is a contradiction, as the following table shows: ‘P v Q’ is not a contradiction, as the following table shows:

  4. math.libretexts.org › Bookshelves › Mathematical1.6: Tautologies and contradictions - Mathematics LibreTexts

    Oct 18, 2021 · In order to know whether Assertion 27 is true, you would need to check the weather. Logically speaking, it could be either true or false, so it is neither a tautology nor a contradiction. Assertion 28 is different. You do not need to look outside to know that it is true, regardless of what the weather is like. So it is a tautology.

  5. math.libretexts.org › Bookshelves › Combinatorics_and1.4: Tautologies and contradictions - Mathematics LibreTexts

    Jan 23, 2022 · Theorem 1.4.1: Substitution Rule. Suppose A is a logical statement involving substatement variables p1, p2, …, pm. If A is logically true or logically false, then so is every statement obtained from A by replacing each statement variable pi by some logical statement Bi, for every possible collection of logical statements B1, B2, …, Bm.

  6. www.javatpoint.com › tautologies-and-contradictionTautologies and Contradiction - Javatpoint

    Tautologies. A proposition P is a tautology if it is true under all circumstances. It means it contains the only T in the final column of its truth table. Example: Prove that the statement (p q) ↔ (∼q ∼p) is a tautology. Solution: Make the truth table of the above statement: p. q. p→q. ~q.

  7. www.mathsisfun.com › proof-by-contradictionProof by Contradiction - Math is Fun

    In a proof by contradiction, the contrary (opposite) is assumed to be true at the start of the proof. After logical reasoning at each step, the assumption is shown not to be true. Example: Prove that you can't always win at chess. Let us start with the contrary: you can always win at chess. I now set up a board, let you take the first move ...

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  9. www.csus.edu › phl4 › handoutsContradiction and Consistency - California State University ...

    Consistency and Contradiction. We say that a statement, or set of statements is logically consistent when it involves no logical contradiction. A logical contradiction is the conjunction of a statement S and its denial not-S. In logic, it is a fundamental law- the law of non contradiction- that a statement and its denial cannot both be true at ...