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# 3 - LECTURE 3 LOGIC(2.1-2.4.when you have eliminated the...

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LECTURE 3: LOGIC ( § 2.1-2.4) ...when you have eliminated the impossible, whatever remains, however improbable, must be the truth. Sir Arthur Conan Doyle (1859 - 1930) 1. Oh say what is truth A statement is a sentence that asserts something that is either true or false (but not both). Example 1. The following are statements: “The sky is blue.” “ π is a real number.” “All dogs are purple.” “The 100th digit of π is 3.” The following are not statements: “Are you happy?” “Give me cake.” “Wow!” We will often use P , Q , and R to denote statements. The truth values are either true (T) or false (F). Example 2. We could let P 1 : 2 = 1 + 1. This is true. We could let P 2 : 3 is even. This is false. Sometimes sentences can depend on variables – we call these open sentences . Example 3. P ( x ) : 3 x = 12 , x Z . This is a true statement, if we plug in x = 4. It is a false statement for any other value of x . We call Z the domain in this case.

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