I completed my BA in Criminal Justice in 2015. Currently working on my MS in Homeland Security Management.
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.
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The P and Q represent the two statements, while the T represents true statements and the F represents false statements.
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).
Here are just a couple more examples of statements that are logically equivalent:
You and your friend discuss an upcoming exam. One of you thinks you do not need to study, while the other one does, here are your statements; 'If I study, I will pass the exam.' and 'If I don't study, I will pass the exam. Both statements have the same meaning or coverage because both statements have to do with passing the exam. Again, neither statement proves one or the other false, so they are logically equivalent.
John thinks Bob is happy he has a car, while Haley thinks Bob is happy because he has a house. Both statements are logically equivalent because both statements cover Bob's happiness, even though each have different reasons for why he is happy.
This lesson covered the basis of understanding what makes two statements logically equivalent We learned that the statements do not have to prove each other true or false, to be equivalent they just need to have the same meaning or coverage. We also learned that analytical reasoning, along with truth charts, help us break down each statement in order determine if two statements are truly logically equivalent. Examples and a truth table were provided in order to better understand the topic.
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LSAT Test: Online Prep & Review11 chapters | 93 lessons | 7 flashcard sets
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