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Recognizing When Two Statements Are Logically Equivalent

Instructor: Jessica Mercado

I completed my BA in Criminal Justice in 2015. Currently working on my MS in Homeland Security Management.

This lesson will cover how to determine when two statements have the same meaning and are logically equivalent. Tools that can be used to determine the logical equivalence of two statements will covered.

Logical Equivalence

Suppose you and your research partner get into an argument over a fruit. You think the fruit is new and exotic because the color is blue. You partner, on the other hand, thinks the fruit is not new and exotic because he does not think the color is blue. Which of you has the right perception?

The right answer is that neither of you are right or wrong, both of your statements are true in their own right. Confusing, right? To have a better understanding of why the two statements are true, one must know the definition of logical equivalence. Logical equivalence occurs when two statements have the same truth value. This means that one statement can be true in its own context, and the second statement can also be true in its own context, they just both have to have the same meaning. In the provided example, the partners are arguing about the same fruit and also about it's color. While the statements may be contradictory, they are logically equivalent because they are covering the same topic. The statements can be derived from one another to determine which is true, which are false, or if both are true or false, based on the topic.

The following table depicts how two statements that are logically equivalent correlate with one another, whether both are true, one is true and one is false, or if both are false. As long as both statements have the same meaning or coverage, then this table holds true and the statements will always be connected and be logically equivalent.

Logical Equivalence Table
Logically Equivalent Table

The P and Q represent the two statements, while the T represents true statements and the F represents false statements.

Analytical Reasoning

A great tool to utilize when determining if two sentences are logically equivalent is analytical reasoning. Analytical reasoning looks at a set of statements, determines the facts and situations associated with those statements and determines what is true or not. Some ways to use analytical reasoning when studying two statements would be; Read each statement carefully to determine the truth value, read each statement as its own independent entity, and highlight text or truth diagrams (i.e. truth tables).

Examples

Here are just a couple more examples of statements that are logically equivalent:

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