Discrete Mathematics

Study guide: Exam P-1

Discrete Mathematics is the branch of mathematics concerned with countable, distinct structures like sets as opposed to continuous quantities studied in calculus.

• It provides the language and tools for counting outcomes, defining events, and reasoning about logical relationships between outcomes and events
• A Power Set \mathcal{P}(S) is the set of all subsets of S:

|\mathcal{P}(S)| = 2^{|S|}

Counting Subsets of a Risk Portfolio An insurer has 4 distinct risk categories: Fire, Flood, Theft, and Liability. How many distinct subsets of these risks could be included in a policy?

Answer The number of subsets of a set with |S| = 4 elements is: |\mathcal{P}(S)| = 2^4 = 16 This includes the empty set (no coverage) and the full set (all four risks covered), giving 16 possible coverage combinations.