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Conditional Statements

Daniel Cole, Yuanxin (Amy) Yang Alcocer
  • Author
    Daniel Cole

    Daniel Cole has taught a variety of philosophy and writing classes since 2012. He received his PhD in philosophy from the University of Kentucky in 2021, his MA in philosophy from Miami University in 2011, and his BA in philosophy from Ball State University in 2008.

  • Instructor
    Yuanxin (Amy) Yang Alcocer

    Amy has a master's degree in secondary education and has been teaching math for over 9 years. Amy has worked with students at all levels from those with special needs to those that are gifted.

Learn about conditional statements. Identify what a conditional statement is, learn how to write a conditional statement, and see conditional statement examples. Updated: 02/25/2022

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What is a Conditional Statement?

What is a conditional statement? Simply put, a conditional statement is an if-then statement, e.g., '"If Jane does her homework, then Jane will get a good grade."' The conditional statement's definition emphasizes a relationship between two ideas, wherein one idea follows from the other. In the example, Jane getting a good grade follows from the idea of Jane doing her homework. Thus, conditional statements are an important part of mathematical and logical reasoning because it allows one to make deductions in a clear and rigorous way.

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  • 0:05 What Are Conditional…
  • 1:05 The Hypothesis
  • 2:04 The Conclusion
  • 2:54 Logic vs. Reality
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How to Write a Conditional Statement?

The question of how to write a conditional statement is not a difficult one. The first requirement is that there are two independent propositions (complete sentences). Then, the terms '"if"' and '"then"' are used in front of those propositions. Note that the meaning of a conditional statement is determined by the if and then but not their order. The proposition that follows the if is called the hypothesis or antecedent, while the proposition that follows the then is called the conclusion or consequent.

To take an example, '"If Jane does her homework, then Jane will get a good grade"' is the same as '"Jane will get a good grade if Jane does her homework."' '"Jane does her homework"' is the hypothesis, and '"Jane will get a good grade"' is the conclusion. In second formulation, the '"then"' is implied while the '"if"' remains explicit. The meaning changes when the if precedes the other idea. The claim that '"If Jane will get a good grade then, Jane will do her homework"' has a different, and perhaps unintuitive, meaning. This sentence suggests that Jane doing her homework depends on her getting a good grade.

Hypothesis and Conclusion of a Conditional Statement

Conditional statements can be symbolized in order to make it easier to manipulate them in logical analysis. Often, an arrow symbol pointing to the right is used to indicate a conditional relationship with the hypothesis of a conditional statement on the left of the arrow and the conclusion on the right. The hypothesis and conclusion are generally symbolized with letters, which act like variables. For example, '"If Jane does her homework, then Jane will get a good grade,"' can be symbolized, {eq}H \rightarrow G {/eq}. The H represents the entire hypothesis, the G represents the conclusion, and the arrow represents the conditional relationship. Thus, there are three conditional statement symbols.

Conditional Statement Logic

Conditional statements in logic are very important, since they set up the basis for many valid argument forms. A valid argument is one in which one can make an inference from premises with certainty. Or in other words, the inference necessarily follows. One of the most commonly used valid argument forms is called modus ponens. In modus ponens, a conditional statement is given along with an affirmation of the hypothesis. From these two premises, it follows that the conclusion must follow. Note that '"conclusion"' is being used in a different sense, as the proposition that follows from one or premises. Modus ponens is expressed as follows:

  • Premise 1: {eq}A \rightarrow B {/eq}
  • Premise 2: A
  • Conclusion: B

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Frequently Asked Questions

How do you write a conditional statement?

Conditional statements are written by connecting two propositions with the words if and then. For example, "if it is winter time, then you will likely hear Christmas carols." is a conditional statement. It can be symbolized by writing the propositions as letters and using an arrow to represent the conditional relationship, A -> B.

What is an example of a conditional statement?

One example of a conditional statement is "If the rug is dirty, then the rug should be vacuumed." "The rug is dirty" is the hypothesis, and "the rug should be vacuumed" is the conclusion.

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