Translate the following arguments into symbolic form. Then use the eighteen rules of inference to derive the conclusion of each. Do not use conditional or indirect proof.
Oranges are sweet. Also, oranges are fragrant. Therefore, oranges are sweet and fragrant. (O, S, F )
Consider the question provided in the textbook:
Statement 1: Oranges are sweet.
Statement 2: Also, oranges are fragrant.
Conclusion: Therefore, oranges are sweet and fragrant.
Consider the symbolized argument:
The conclusion is derived as follows:
Apply the rule of universal initialization on line 1:
Apply rule of universal initialization on line 2:
Apply rule of material implication on lines 3 and 4:
Apply rule of conjunction combining lines 5 and 6:
Apply rule of Distribution on line 7 as follows:
Apply rule of material implication on line 8:
Apply rule of universal generalization on line 9:
Therefore, the argument is completed as follows: