Question

1. A job ad for Gaggle Inc. says that it is necessary to major in math, computer science, or philosophy, and be an A or B student. However, Gaggle makes an exception and does not have any grade requirements if you have won a Turing award or Fields Medal (they still have the major requirements). You have also heard through the grapevine that it is sufficient that you are in one of these 3 majors and an A student.

   Express the above as one PC wff. You should of course state what your atoms represent. Please do not do any form of reasoning to simplify the wff – that’s not the point here, and may also introduce bugs.

Answer 1

Wffs

We define well-formed-formula (wffs) inductively:

1. Every primitive (atomic) proposition is a wff
2. If is a off, is is
3. If and are wffs, so are and

First find appropriate primitive propositions:

1. : Major in math
2. : Major in computer science
3. : Major in philosophy
4. : be an A student
5. : be an B student
6. : Won a Turing award
7. : Won a Fields Medal

Now that we defined our primitive proposition, let's translate the Gaggle Inc. job requirement to wffs.

First requirement: major in math, computer science, or philosophy, and be an A or B student.

Translation to wff :

Second requirement : have won a Turing award or Fields Medal and are major in one of the three subjects

Translation to wff :

Since a candidate for the job has to satisfy either of the two requirements, the or of the two wff is the required condition to qualify for the job. Thus our wff is:

grapevine requirement : major in one of the three subject and be an A student

Translation to wff :