Discrete Math Logical Equivalence
Logical equivalence is a type of relationship between two statements or sentences in propositional logic or Boolean algebra.
You can’t get very far in logic without talking about propositional logic also known as propositional calculus.
A proposition is a declarative sentence (a sentence that declares a fact) that is either true or false.
Examples of propositions:
- Tallahassee is the capital of Florida
- Washington D.C. is not the capital of the United States
- 0 + 2 = 2
- 2 + 3 = 10
Propositions 1 and 3 are true, while propositions 2 and 4 are false, not both true and false.
We use letters to denote propositional variables, similar to how letters can represent numbers. The conventional letters used are p,q,r,s,….. The truth value of a proposition is denoted by T and false value by F.
Truth Table
A truth table is a mathematical table used in logic specifically in connection with Boolean algebra, boolean functions, and propositional calculus to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of values taken by their logical variables (Enderton, 2001). In…
