Final answer:
A valid argument can have a false conclusion if the premises are false. Validity refers to the logical structure where if the premises are true, the conclusion must be true, but it does not concern the actual truth of the premises or conclusion.
Step-by-step explanation:
To answer whether a valid argument can have a false conclusion, we must understand the distinction between validity and truth. An argument is valid if the form of the argument is such that if the premises were true, the conclusion must be true as well. This means answer choice c) Yes, if premises are false but logically lead to the conclusion is incorrect because if the premises are false, the argument does not guarantee the truth of the conclusion. However, a valid argument can have a false conclusion if the premises themselves are indeed false. This is because validity is solely concerned with the logical structure and whether the conclusion logically follows from the premises.
An example of a valid argument is a Disjunctive Syllogism:
- X or Y.
- Not Y.
- Therefore X.
If the premises here are true, the conclusion must follow. However, if the premises are false (e.g., Y is actually true), the conclusion could also be false, yet the argument remains valid because of its correct logical form. Thus, validity does not depend on the actual truth of the premises or conclusion; it depends on whether the premises, if true, logically necessitate the conclusion.
Answer choice a) Yes, if premises are true but do not support the conclusion is incorrect because if the premises are true but do not support the conclusion, the argument is not valid. Answer choice d) No, as validity requires both true premises and a true conclusion is also incorrect because validity does not require the premises or conclusion to be true, only that if the premises are true, the conclusion must be. Therefore, the correct answer is b) No, as validity guarantees a true conclusion. If the premises of a valid argument are true, then it must have a true conclusion; however, a valid argument can have false premises and consequently a false conclusion.