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MATH 301 – HOMEWORK II


1. Translate the following stories into symbols, then draw a truth table to test the validity of the argument form.

(a) I shall mow the lawn or clean the car, but not both. If I mow the lawn, then it won’t rain. Therefore, it rains only if I clean the car.

(b) If I buy a new car, then I will not go on holiday. If I don’t buy a new car, then I will buy a motorcycle. Therefore, either I go on holiday or I buy a motorcycle, but not both.


2. Translate the following stories into symbols, then provide a formal proof of the validity of each argument.

(a) If she drinks wine or eats cheese, she gets a terrible headache. She is drinking wine and eating chocolate. Therefore, she will get a terrible headache.

(b) If the battery is dead or the car is out of gas, then it won’t start and I will be late for class. Either the car is out of gas or the battery is dead. Therefore, I will be late for class.

(c) Peter is either brave or brainy. Peter is also brainy or bald. Peter isn’t brainy. Therefore, he is brave and bald.