Symbolic Logic#
Propositions#
Truth Tables
Construct a truth table to determine if the following symbolic propositions are tautologies, contradictions or contingencies.
TODO
TODO
TODO
TODO
Carnap’s Method
Use carnaps_method to determine if the following symbolic propositions are tautologies, contradictions or contingencies.
TODO
TODO
TODO
TODO
Symbolic Arguments#
Construct a truth table to determine if the following arguments are tautologies, contradictions or contingencies.
TODO
TODO
TODO
TODO
TODO
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!
Suppose the proposition “All things which are A are also B” is true. Determine the truth-values of the following propositions, if possible.
“No things which are A are also not B”
“All things which are not A are also not B”
“No things which are B are also A”
“Some things which are not B are also A”
“Some things which are not A are also B”
Suppose the proposition “No things which are A are also B” is true. Determine the truth-values of the following propositions, if possible.
“Some things which are not B are also not A”
“All things which are not A are also not B”
“No things which are not A are also not B”
“Some things which are not B are also A”
“All things which are not B are also not A”
Suppose the proposition “Some things which are A are also B” is true. Determine the truth-values of the following propositions, if possible.
“All things which are A are also not B”
“Some things which are A are also not B”
“No things which are B are also A”
“Some things which are B are also A”
“No things which are A are also not B”
Suppose the proposition “Some things which are A are also not B” is true. Determine the truth-values of the following propositions, if possible.
“All things which are A are also not B”
“Some things which are A are also not B”
“No things which are not A are also B”
“No things which are not B are also A”
“Some things which are B are also A”