I was given two predicates $text{Prime}(x)$ and $text{Even}(x)$ and is required to write the following statements:

- For every odd natural number there is a different natural number such that their sum is even.

My attempt: $(forall x):(x in mathbb{N} wedge neg text{Even}(x) to (exists y):(x neq y wedge text{Even}(x+y))).$

and

- The sum of any two prime numbers except the prime number $2$ is even.

My attempt: $(forall x,y):(x neq 2 wedge yneq 2 wedge text{Prime}(x,y) to text{Even}(x+y)).$

Is my attempt correct? And Am I allowed to write $text{Prime}(x,y)$ or should I write $(text{Prime}(x) wedge text{Prime}(y))?$

Mathematics Asked by starry on December 29, 2020

1 AnswersIn the first statement, you wrote $x neq y wedge text{Prime}(x+y)$ but it should be $x neq y wedge text{Even}(x+y).$

Avoid writing $text{Prime}(x,y)$ because the predicate $text{Prime}$ only takes one argument (i.e., $text{Prime}(x)$.)

You could also have written the following.

$(forall x in mathbb{N})(exists y in mathbb{N}):[neg text{Even}(x) to (x neq y wedge text{Even}(x+y))].$

$(forall x in mathbb{N})(forall y in mathbb{N}):[(text{Prime}(x) wedge text{Prime}(y) wedge x neq 2 wedge y neq 2) to text{Even}(x+y)].$

Answered by Air Mike on December 29, 2020

1 Asked on November 1, 2021

3 Asked on November 1, 2021 by user31415

2 Asked on November 1, 2021 by user809806

5 Asked on November 1, 2021 by maomao

combinatorial geometry combinatorics geometry recreational mathematics

3 Asked on November 1, 2021

abstract algebra finite groups group theory reference request

3 Asked on November 1, 2021 by eureka

1 Asked on November 1, 2021 by user801681

4 Asked on November 1, 2021 by user768934

calculus definite integrals integration trigonometric integrals

18 Asked on November 1, 2021 by aman_cc

3 Asked on November 1, 2021 by claude-leibovici

2 Asked on November 1, 2021 by kdbanman

3 Asked on November 1, 2021 by hugseirvak

2 Asked on November 1, 2021 by hazim

2 Asked on November 1, 2021 by user579861

1 Asked on November 1, 2021 by ttl

1 Asked on November 1, 2021 by kufs

characteristic polynomial linear algebra minimal polynomials

1 Asked on November 1, 2021 by nomadicmathematician

measure theory probability theory real analysis stochastic processes

1 Asked on November 1, 2021

2 Asked on November 1, 2021 by hk1510

Get help from others!

Recent Answers

- DMGregory on MouseLook Script “Pops” back to the last value when the script is enabled after being disabled or destroyed
- haakon.io on Why fry rice before boiling?
- Joshua Engel on Why fry rice before boiling?
- Jon Church on Why fry rice before boiling?
- Peter Machado on Why fry rice before boiling?

Recent Questions

- Why fry rice before boiling?
- MouseLook Script “Pops” back to the last value when the script is enabled after being disabled or destroyed
- Unity app crashes when using unmodified custom Android manifest (didn’t find class “UnityPlayerActivity”)
- How do i draw a ray in unity
- How to test consistency of responses?

© 2022 AnswerBun.com. All rights reserved.