Question

For the argument below, perform the following a) Translate the argument into symbolic form. b) Determine if the argument is valid or invalid. Compare the argument to a standard form or use a truth table. If we study longer, then we will do well on the test. We will do well on the test. ∴ We studied longer.

Answer 1

Main Answer:

a) If we study longer (p), then we will do well on the test (q). We will do well on the test (q). ∴ We studied longer (p).

b) Valid.

Step-by-step explanation:

The argument is valid because it follows the logical structure of a valid argument known as modus ponens. In symbolic form, if p (we study longer), then q (we will do well on the test), and q (we will do well on the test) is asserted, the conclusion logically follows that p (we studied longer). This is a valid deduction based on the established premises.

The argument aligns with the standard form of modus ponens, a fundamental rule of inference in propositional logic. In this case, the truth of the premises guarantees the truth of the conclusion. It's akin to saying, if a specific condition (studying longer) leads to a certain outcome (doing well on the test), and that outcome is realized (we did well on the test), then the condition (we studied longer) must have been met.

In summary, the argument is structurally sound and adheres to the principles of logical reasoning, making it valid.