Fundamentals of Computer Science - Week 2 (Essential reading) - Part 1 out of 2

Propositional Equivalences

An important type of step used in a mathematical argument is the replacement of a statement with another statement with the same truth value. Note that we will use the term “compound proposi- tion” to refer to an expression formed from propositional variables using logical operators, such as p ∧ q.

Tautology: compound proposition that is always true
Contradiction: compound proposition that is always false
Contingency: compound proposition that is neither tautology nor a contradiction

Logical Equivalences

Compound propositions that have the same truth values in all possible cases are called logically equivalent. We can also define this notion as follows:

> The compound propositions p and q are called logically equivalent if p ↔ q is a tautology. The notation p ≡ q denotes that p and q are logically equivalent.





Propositional Satisfiability

An unsatisfiable compound proposition happens when the negation is a tautology.
A satisfiable compound proposition is satisfiable if there is an assignment of truth values to its variables that makes it true.


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