Chapter 2 Section 2: Conditional Statements

Study Notes

Conditional Statements

A conditional statement is expressed as "If p then q" or "p implies q," denoted as p → q.
The truth value of a conditional is false only when p is true and q is false; it is true in all other scenarios.
In a conditional, p is known as the hypothesis or antecedent, while q is the conclusion or consequent.

Negation of a Conditional

The negation of "if p then q" is equivalent to "p and not q," indicating when the original statement is not true.

Contrapositive

The contrapositive of a conditional statement "If p then q" is written as "If not q then not p," symbolically represented as ∼q → ∼p.
The contrapositive logically carries the same truth value as the original conditional statement.

Converse

The converse of a statement "if p then q" is formed by reversing the order to "if q then p."

Inverse

The inverse of the statement "if p then q" is created by negating both parts, resulting in "if not p then not q."

Only If

The phrase "p only if q" is logically interpreted as "if not q then not p," which is also equivalent to "if p then q."

Biconditional

A biconditional statement is expressed as "p if and only if q," denoted as p ↔ q.
It is deemed true when both p and q possess the same truth values and false if they differ.

Order of Operations

The hierarchy for evaluating logical expressions follows this order:
- Negations have the highest priority.
- Followed by conjunctions (ands) and disjunctions (ors).
- Conditionals come last in the order of operations.

Description

Test your understanding of conditional statements with flashcards covering key concepts like implications and negations. This quiz will help solidify your knowledge on the logical structure of conditionals and their components. Ideal for students learning basic logic and reasoning.