Learn

Conditional Statements

A conditional statement is a statement that can be written in if-then form. Example: If it is snowing, then it is cold outside. The hypothesis (such as it is snowing) of the conditional statement is the phrase following “if”. It tells what condition must be met. The conclusion (such as it is cold outside) of the conditional statement is the phrase following then. It tells what will happen if the condition is met.

Conditional Statements Reworded

Conditional statements can also be worded in different ways.

Example: It is cold outside if it is snowing. A snowy day is a cold day.

Even though these sentences are worded differently, the hypothesis and the conclusion are the same.

Converse

The converse of a conditional statement is written by switching the hypothesis and conclusion.

Conditional: If it is snowing, then it is cold outside.
Converse: If it is cold outside, then it is snowing.

The converse will not necessarily be a true statement, as you can see with this example. The temperature outside could be 38 degrees, which means it would be cold, but it would not be snowing. Remember: one counterexample makes it false.

Knowledge Check #1

Conditional:
If you live in Birmingham, then you live in Alabama. What is the hypothesis of this statement?

  1. You live in Alabama
  2. You live in Birmingham
  3. If you live in Birmingham
  4. Then you live in Alabama

Answer: b. You live in Birmingham

Knowledge Check #2

Conditional:
If you live in Birmingham, then you live in Alabama. What is the conclusion of this statement?

  1. You live in Alabama
  2. You live in Birmingham
  3. If you live in Birmingham
  4. Then you live in Alabama

Answer: a. You live in Alabama

Knowledge Check #3

Conditional:
If you live in Birmingham, then you live in Alabama. What is the converse of this statement?

  1. You live in Alabama if you live in Birmingham.
  2. You live in Alabama.
  3. If you live in Alabama, then you live in Birmingham.
  4. People who live in Birmingham live in Alabama.

Answer: c. If you live in Alabama, then you live in Birmingham.

Knowledge Check #4

Conditional:
If you live in Birmingham, then you live in Alabama. Converse:
If you live in Alabama, then you live in Birmingham. Is the converse true or false?

Think of a counterexample.
Any specific city in Alabama other than Birmingham would be a counterexample. Such as: Dothan, Tuscumbia, Fort Payne, Huntsville, Clanton, Auburn, Fayette, Demopolis, Gulf Shores,, or Tuscaloosa.

  1. True
  2. False

Answer: b. False