Logic

Logic#

Propositions#

  1. Truth Tables

Construct a truth table to determine if the following symbolic propositions are tautologies, contradictions or contingencies.

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  1. Carnap’s Method

Use Carnap’s Method of Tautology to determine if the following symbolic propositions are tautologies, contradictions or contingencies.

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Symbolic Arguments#

  1. Construct a truth table to determine if the following arguments are tautologies, contradictions or contingencies.

    1. TODO

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Aristotle’s Square of Opposition#

Hint

For the following problems, find an interpretation of the given proposition that obtains truth in the real world.

For example, in the first problem, let

A ~ The set of humans

B ~ The set of mammals

Then the proposition “All things which are A are also B” becomes “All humans are also mammals”. This will make interpretting the subsequent propositions easier!

  1. Suppose the proposition “All things which are A are also B” is true. Determine the truth-values of the following propositions, if possible.

    1. “No things which are A are also not B”

    2. “All things which are not A are also not B”

    3. “No things which are B are also A”

    4. “Some things which are not B are also A”

    5. “Some things which are not A are also B”

  2. Suppose the proposition “No things which are A are also B” is true. Determine the truth-values of the following propositions, if possible.

    1. “Some things which are not B are also not A”

    2. “All things which are not A are also not B”

    3. “No things which are not A are also not B”

    4. “Some things which are not B are also A”

    5. “All things which are not B are also not A”

  3. Suppose the proposition “Some things which are A are also B” is true. Determine the truth-values of the following propositions, if possible.

    1. “All things which are A are also not B”

    2. “Some things which are A are also not B”

    3. “No things which are B are also A”

    4. “Some things which are B are also A”

    5. “No things which are A are also not B”

  4. Suppose the proposition “Some things which are A are also not B” is true. Determine the truth-values of the following propositions, if possible.

    1. “All things which are A are also not B”

    2. “Some things which are A are also not B”

    3. “No things which are not A are also B”

    4. “No things which are not B are also A”

    5. “Some things which are B are also A”

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