# Often the universal quantier needed for a precise

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Unformatted text preview: Example: Our domain consists of all students and c: Alice is a student. “There is a student who got an A in the course.” “Therefore, Alice got an A in the course.” Existen\$al Generaliza\$on (EG) Example: “Alice got an A in the class.” “Therefore, There is a student who got an A in the class.” Using Rules of Inference Example 1: construct a valid argument to show that “John Smith has two legs.” is a consequence of the premises: “Every man has two legs.” “John Smith is a man.” Solution: Let M(x) denote “x is a man” and L(x) “x has two legs” and let John Smith be a member of the domain Using Rules of Inference Example 2: construct a valid argument showing that “Someone who passed the ﬁrst exam has not read the book.” follows from the premises “A student in this class has not read the book.” “Everyone in this class passed the ﬁrst exam.” Solution: Let C(x) denote “x is in this class,” B(x) denote “ x has read the book,” and P(x) denote “x passed the ﬁrst exam.” Using Rules of Infe. Solu\$on for Socrates Example Proofs of Mathema\$cal Statements ༉  Proof is a valid argument that shows the truth of a statement. ༉  In math, CS, and other disciplines, informal proofs are used. ༉  ༉  ༉  ༉  ༉  More than one rule of inference are often used in a step. Steps may be skipped. The rules of inference used are not explici...
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