I'm supposed to symbolize (Quantificational Notation) and construct a proof for a few arguments which have me stumped.

For instance: -Two is the only even prime number, and no even prime number is greater than three. Therefore, if four is an even prime number, it is equal to two and not greater than three.

I may be doing this entirely wrong, as math and logic are not my forte, but this is as far as I get in writing out the initial statements, before constructing the proof:

  1. (N2 • P2 • E2) • (____________) <--- from what I understand about identity, "Exactly" is a combination of "At least and "At most" - I'm not sure how to write an "At most" statement using 2 as I've only ever done it with (x) (y) ( [etc} 2.~(x) Nx• Px • Ex > 3

:. (therefore) N4 • E4 • P4 --> 4=2 • 4 ≯ 3

Does this make sense? Please help!


For 1, after having stated that $2$ is an even prime number, add that 'if anything is an even prime number, then it equals $2$'

For 2, you need to negate an existential, i.e. 'there is not some prime even number greater than $3$'. Also, don't say $Ex>3$ ... now you're mixing up two statements. Instead, use $Ex \cdot x > 3$

Your conclusion looks fine.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.