How can I write 'the number 100 can be written as the sum of 2 squares' into a logical proposition?

I'm starting with the basics of discrete mathematics and am not sure from what angle to approach it.

We've started learning about existential statements so I assume that would be the ideal approach? Not sure though - would appreciate a hand to approaching similar questions.

  • 1
    $\begingroup$ Not sure if this is what you want but $\exists x, y$ such that $x^2 + y^2 = 100.$ You can further specify what ring you want the numbers from. $\endgroup$ – 伽罗瓦 Aug 8 '17 at 11:20

If you are talking about propositional logic, the answer is simple: $p$.

But I guess that you are talking about predicate logic. Then you have predicates and quantifiers. I'll use also standard symbols for certain predicates, such as $=$ and $\in\Bbb N$. The statement becomes $$\exists x(\exists y( x\in \Bbb N\wedge y\in \Bbb N \wedge x^2+y^2=100))$$


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.