![]() The clause associated with the "if" statement is also called the hypothesis or antecedent, while the clause following the "then" statement or the word implies is called the conclusion or consequent. Joining two logical statements with the word implies, or using the phrase “if first statement, then second statement,” is called a conditional or implication. Inclusive or means you can have one, or the other, or both! This disjunction is true if the office manager ordered only cake, only ice cream, or they ordered both cake and ice cream. Consider the compound statement, "The office manager ordered cake for for an employee’s birthday or they ordered ice cream.” This is a disjunction because it combines the independent clause, “The office manager ordered cake for an employee’s birthday,” with the independent clause, “The office manager ordered ice cream,” using the connective, or. Unless otherwise specified, a disjunction is an inclusive or statement, which means the compound statement formed by joining two independent clauses with the word or will be true if a least one of the clauses is true. The joining of two logical statements with the word “or” forms a compound statement called a disjunction. Consider the compound statement, “Derek Jeter played professional baseball for the New York Yankees, and he was a shortstop.” If p p represents the statement, “Derrick Jeter played professional baseball for the New York Yankees,” and if q q represents the statement, “Derrick Jeter was a short stop,” then the conjunction will be written symbolically as p ∧ q. In logic, for a conjunction to be true, all the independent logical statements that make it up must be true. ![]() The joining of two logical statements with the word "and" or "but" forms a compound statement called a conjunction. The chapter will discuss each connective introduced here in more detail. Understanding the following logical connectives, along with their properties, symbols, and names, will be key to applying the topics presented in this chapter. It also explores the order of operations, or dominance of connectives, when a single compound statement uses multiple connectives. This section introduces common logical connectives and their symbols, and allows you to practice translating compound statements between words and symbols. So, did your friend acquire their driving license?. The second independent clause in this compound statement is, “My friend did not pass the road test.” The word "but" is the connective used to join these two statements together, forming a compound statement. The statement, “My friend passed the written test,” is an independent clause because it is a complete thought or idea that can stand on its own. After passing the written test, your friend must also pass a road test to demonstrate that they can perform the physical task of driving safely within the rules of the law.Ĭonsider the statement: "My friend passed the written test, but they did not pass the road test." This is an example of a compound statement, a statement formed by using a connective to join two independent clauses or logical statements. In most places, they will need to pass some form of written test proving their knowledge of the laws and rules for driving safely. Suppose your friend is trying to get a license to drive. ![]() Translate compound statements in symbolic form with parentheses into words.Translate compound statements into symbolic form.(credit: modification of work “Drivers License -Teen driver” by State Farm/Flickr, CC BY 2.0) Learning ObjectivesĪfter completing this section, you should be able to: A compound statement can be used to explain performance on both tests at once. Figure 2.6 A person seeking their driver's license must pass two tests.
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