/sci/ - Science & Math

Halp. This is a logic question.

Where A is a quanti er free sentence, prove by induction that a set containing all the atomic subsentences of a sentence A either implies A or implies  A. Give the basis case, the case where A is a negation, and the case where A is a disjunction.

I have an exam tomorrow and this is going to be on there, but I'm going full retard and can't seem to prove this.

Race: cat
Gender: male
Country: cat
Age: 4
IQ if taken: cat
Major: cat
cat

/discuss
(pic unrelated)