Final answer:
The conclusion's validity can be determined using the Law of Detachment or the Law of Syllogism, depending on the premise-conclusion structure. The Law of Detachment applies to direct conditional cases, while the Law of Syllogism applies to transitive conditional relationships. An invalid conclusion does not logically follow from its premises.
Step-by-step explanation:
To assess the validity of a conclusion based on given premises and identify which logical law is utilized, we look at two specific logical laws: the Law of Detachment and the Law of Syllogism.
The Law of Detachment, also known as modus ponens, follows this structure: If 'if P then Q' is true, and P is true, then Q must also be true. If an inference observes this structure, the conclusion drawn from it is valid using the Law of Detachment.
The Law of Syllogism, similar to a transitive property in mathematics, lets you deduce a conclusion from two conditional statements when the conclusion of the first statement is the premise of the second. In other words, if 'if P then Q' and 'if Q then R' are both true, then we can deduce that 'if P then R' is true. This conclusion would be valid by the Law of Syllogism.
An invalid conclusion results when the structure of the argument does not match the necessary form of a valid deductive inference. If applying this detail to an example, and the conclusion does not logically follow from the premises, even when the premises are true, the argument is invalid.