Answer to Question #260450 in Discrete Mathematics for jDoes369

Question

Consider the following two arguments:

A. If Fred wanted me fired then he would go to the boss. Fred is going to the boss. Therefore Fred wants to get me fired.

B. Max is a cat or Max is a mammal. Max is a cat. Therefore Max is not a mammal.

Which of the following is true?

Answer 1

A) Let $A$ be a proposition "Fred wanted me fired", $B$ is proposition "Fred is going to the boss". So the proposition "If Fred wanted me fired then he would go to the boss" is $A\mapsto B.$ We have that$A\mapsto B$ is true and $B$ is true. If $A$ is false, the proposition $A\mapsto B$ also is true because a lie can lead to both truth and falsehood. So $A$ can be false.

B) Let $A$ be a proposition "Max is a cat" , $B$ is propsition "Max is a mammal". We have two arguments: $A\lor B, B$  that are true. If B is true, we have that $A\lor B$ also is true and  $A$  can be true of false. But Max can't be a cat and a mammal simultaneously in a real life. So the proposition $\lnot A$ is true.