Symbolic logic is the simplest form of logic. Developed by George Boole, symbolic logic's main advantage is that it allows operations -- similar to algebra -- to work on the truth values of its propositions. Symbolic logic is used in argumentation, hardware and software development and many different disciplines. Being able to translate sentences into symbolic logic will help you develop a better understanding of arguments and logical processes overall.
Separate sentences in a group with propositions and a group with sentences that are not propositions. A proposition is a sentence that cannot be reduced without losing its meaning. Propositions are the building blocks of symbolic logic and can be evaluated as True or False. Capital letters are used as symbols for propositions. For example, "Jack is 20 years old" is a proposition because it is factual; "The Lakers are the best team" is not a proposition because it is an opinion. Propositions are represented by capital letters such as "S" and "P."
Find the sentences that contain the words "no," "not" or phrases such as "it is not true," "it is false" or any phrase that negates the statement. This is called the negation operator. For example: "Jack is not 20 years old." The proposition is "S." The phrase will be "not S." "He didn't travel south." The proposition is "R." The phrase will be "not R."
Identify sentences that contain the words "and" and "or." Separate each part of a sentence and divide it by an "and" or "or" into two or more statements. "And" is a conjunction, "or" is a disjunction, and they are applied between two or more statements. See the California State University, San Bernardino, website for the different values on the Truth tables for conjunctions and disjunctions. Keep in mind that commas can mean "and" or "or" depending on the context. For example: "Apples are red and green." Separate into "Apples are red and apples are green." These are two propositions "S and R." "Cars are small, medium or large." Separate into "Cars are small, or cars are medium, or cars are large." These are three propositions: "A or B or C."
Identify sentences that have conditional statements. A conditional statement has the form "if.... then..." These statements are applied to two propositions. Keep in mind that the statements can be in any order. For example: "If it is overcast, then it will rain." Propositions: "It is overcast" (S), "it will rain" (Q) translates to "if S then Q." "I will get an A if I have the time to study." Propositions: "I will get an A" (T), "I have time to study" (U) translates to "if S then U."
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