Final answer:
Examples of propositional knowledge include factual information such as mathematical formulas, the U.S. states, and the list of U.S. presidents. It can be a priori or a posteriori knowledge, distinguished by being gained through reason or experience respectively.
Step-by-step explanation:
Examples of propositional knowledge would include mathematical formulas, the individual states comprising the United States, and the listing of the U.S. presidents. Propositional knowledge is understanding facts and truths about the world, often described as "knowledge that." For instance, knowing mathematical formulas is achieved through a system of symbols and rules that operate within mathematics. Similarly, learning the states of the U.S. or the list of presidents involves remembering specific facts that are accurate and verifiable. This type of knowledge can be a priori, which is gained through reason alone, like mathematical formulas, or a posteriori, which is gained through experience, like recalling the shortest route to a nearby restroom.
Logical knowledge, on the other hand, is understanding the relationship of ideas to each other, governed by the rules of logic. In history classes, concepts like democracy and freedom are discussed explicitly, which helps to crystallize these types of knowledge.