Identify the Error in Logical Inference: Discrete Math Exercise 14
The exercise presents an argument based on logic where it is incorrectly concluded that Lola is happy based on the given premise. The solution points out that while there exists an x that satisfies the premise, it does not necessarily mean Lola is one such x. This highlights the importance of careful reasoning in logical inference.
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Discrete Math: Rules of Inference Exercise 14
Exercise What is wrong with this argument? Let H(x) be x is happy. Given the premise x H (x ), we conclude that H (Lola). Therefore, Lola is happy.
Solution We know that some x exists that makes H(x) true, but we cannot conclude that Lola is one such x. Maybe only Suzanne is happy and everyone else is not happy. Then x H(x) is true, but H(Lola) is false.
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
