Final answer:
The situation with Carolyn not buying a pair of shoes and therefore not getting a discount on a second pair is an example of a valid disjunctive syllogism. In deductive reasoning, if a condition is not met, then the outcome dependent on that condition will not occur, making the argument valid.
Step-by-step explanation:
The scenario provided describes a conditional promotion where purchasing one pair of shoes would lead to a discount on a second pair. Specifically, it outlines that if a person buys one pair, they can get another pair for 50% off. However, the statement given is that Carolyn does not buy one pair of shoes, and therefore, she does not receive the 50% discount on a second pair.
This is an example of a disjunctive syllogism, which is a common form of valid deductive reasoning. However, the argument itself, in this case, is presenting a situation without a logical contradiction because it does not involve making a deduction based on two contradictory statements. It is simply stating that since the initial condition of buying a pair of shoes is not met, the consequence (getting another pair for 50% off) does not follow.
Thus, the syllogism here can be considered valid as it adheres to the rules of deductive reasoning. If the first condition (buying one pair of shoes) is not met, then the conclusion (getting the discount) does not occur, and that aligns with the logical structure of a conditional statement.