Final answer:
A conjecture is a statement presumed true based on logical reasoning. In logical arguments, premises support a conclusion, which can be a conjecture before being proven. Counterexamples help disprove statements by showing a breach in necessary and sufficient conditions.
Step-by-step explanation:
A conjecture is a statement that you conclude to be true based on logical reasoning. When exploring logical statements such as conditionals or universal affirmative statements, a conjecture serves as a tentative conclusion derived from inductive reasoning. As you gather evidence or premises to support a claim, your eventual conclusion might initially be a conjecture, particularly before you have definitive proof.
In the discipline of logic, an argument is composed of premises that support a conclusion. The conclusion is the claim being asserted as true, and the premises are the evidence or reasoning provided to support that claim. An important aspect of a logical argument is the inference—the process that connects the premises to the conclusion. If an inference is strong, and the premises are true, the conclusion is likely to be true as well. Conversely, if the premises do not logically lead to the conclusion, even if they are true, the argument is considered to be invalid.
In summary, to demonstrate the falseness of a conditional or universal affirmative statement, one must present a counterexample that shows the necessary and sufficient conditions do not hold. This indicates that logical reasoning and evidence are critical in establishing the strength and validity of arguments.