Translating an argument into symbolic logic > a. Write the following argument in symbolic logic. > > If Ryan gets the office position and works hard, then he will get a bonus. If he gets a bonus, then he will go on a trip. He did not go on a trip. Therefore, either he did not get the office position or he did not work hard. > > b. Use logical equivalences to determine if the argument is valid or invalid. So.... I have an answer for a, but I am having troubles understanding what they are looking for in b, any ideas? The following is my answer for a... Answer for a: Let: * $A$ = Gets office position * $B$ = Works hard * $C$ = Gets a bonus * $D$ = Go on a trip Then: $$((A \land B) \to C) \land (C \to D) \land (\neg D),\therefore ((\neg A) \lor (\neg B))$$

* first, do you believe the the argument is true? And how did you come to that belief? (that might help later when you do symbolic manipulation)

* 'using logical equivalences' means replace parts of the sentence with equal parts. e.g. $X \rightarrow Y$ can be replaced by $\
eg X \lor Y$

* the [kinds of equivalences you might use here...modus tollens: replace $X\rightarrow Y$ with $\
eg Y \rightarrow \lnot X$ (that's a true equivalence, right?) and $W \land (W \lor Z)$ with $W$. Repeat until you get what you want.




For example of modus tollens, if as part of a larger statement, you can replace $(X\rightarrow Y) \land \
eg Y$ with $\
eg X$ because they are equivalent (because given that $X$ implies $Y$, if you also know that $Y$ is false then you can infer that $X$ cannot be true, so $\
eg X$ is true).