Discrete Math Rules of Inference Exercise on Socrates
This exercise illustrates the valid argument form known as modus ponens through the example of Socrates. It states that if Socrates is human, then he is mortal. Given the premise that Socrates is human, the conclusion must follow that Socrates is mortal. The assessment confirms that if the premises are true, the conclusion is also true, showcasing the foundational principles of logical reasoning in discrete mathematics.
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Discrete Math: Rules of Inference Exercise 1
Exercise Find the argument form for the following argument and determine whether it is valid. Can we conclude that the conclusion is true if the premises are true? If Socrates is human, then Socrates is mortal. Socrates is human. _____________________________________________________ Socrates is mortal.
Solution This is modus ponens. The first statement is p q, where p is "Socrates is human" and q is "Socrates is mortal." The second statement is p. The third is q. Modus ponens is valid. We can therefore conclude that the conclusion of the argument (third statement) is true, because the hypotheses (the first two statements) are true.
References Discrete Mathematics and Its Applications, McGraw-Hill; 7th edition (June 26, 2006). Kenneth Rosen Discrete Mathematics An Open Introduction, 2nd edition. Oscar Le in A Short Course in Discrete Mathematics, 01 Dec 2004, Edward Bender & S. Gill Williamson
