Final answer:
The law of noncontradiction logically implies the law of the excluded middle by ruling out a middle option and leaving only two possibilities: a statement is true or its negation is true, which underpins normative logical reasoning.
Step-by-step explanation:
The law of noncontradiction states that contradictory propositions cannot both be true at the same time and in the same sense. For example, the statement 'My dog is on her bed' and its negation 'My dog is not on her bed' cannot both be true simultaneously. This logical law implies the law of the excluded middle by eliminating the possibility of a middle or third option in the truth value of a statement. Since a proposition and its negation cannot both be true, we are left with only two possibilities: either the proposition is true, or its negation is true, hence excluding any middle position between being true and not true. This relationship between these laws is foundational to reasoning and is considered normative, as logic dictates how we ought to reason. An example of a conditional statement is 'If it is raining, then the ground is wet.' Here, the condition necessary for the ground being wet is the fact that it is raining, while the fact that it is raining is sufficient to conclude that the ground is wet. A counterexample, in logic, is an instance that shows a proposition or theory to be false.