Given: A
¬A
Prove: B
Step | Justification |
---|---|
A ∧ ¬A | Assumed |
(A ∧ ¬A) ∨ B | The first clause is true, therefore the first clause or the second clause is true. |
¬¬((A ∧ ¬A) ∨ B) | A double negative is an affirmation |
¬(¬(A ∧ ¬A) ∧ ¬B) | DeMorgan's Laws |
¬((¬A ∨ A) ∧ ¬B) | DeMorgan's Laws |
¬((TRUE) ∧ ¬B) | Law of the Excluded Middle |
¬(¬B) | The truth of the conjunction is equivalent to the second clause. |
B | A double negative is an affirmation |
Any line of argument is susceptible to error. More confidence may be placed in a conclusion supported by multiple lines of argument.
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