# English into logic statement

1. Jan 23, 2016

### cragar

1. The problem statement, all variables and given/known data
Express the following English sentence as a symbolic statement.
Do not use the there exist symbol
“There is a unique natural number n which is both even and prime.”

We also have properties like
let P(n) be the property that n is prime, L(n, m) the relation that n < m, and E(n) the property that n is even.
3. The attempt at a solution
$\forall n (E(n) and P(n) and n<3)$

2. Jan 23, 2016

### Jeff Rosenbury

Perhaps I'm under-thinking this: 2.

It doesn't convey all the information of the original, but any sentence that does will evaluate to 2. And most will reduce to 2 as well.

3. Jan 23, 2016

### PeroK

What about first changing the English version into saying what is not true?

I interpret your symbolic statement (attempted solution) to mean: all natural numbers are even, prime and less than 3.

4. Jan 23, 2016

### haruspex

How do you write that in symbols?

5. Jan 23, 2016

### cragar

Would it work to say that $n \in \mathbb{N}$
$n \in \mathbb{N} : (P(n) \& E(n))$

6. Jan 23, 2016

### haruspex

No, you must represent "there is" somehow. Are you not aware of a symbol for that?

7. Jan 23, 2016

### cragar

the only symbol I am aware of is there exists $\exists$ but we were told tonot use it in the problem.
Im not sure of a symbol for that

8. Jan 23, 2016

### haruspex

Sorry, I overlooked that.
In that case, as others have suggested, you can get around it by making explicit reference to that number. One part of your answer will express that 2 has these properties. What will the rest of your answer state?

9. Jan 24, 2016

### PeroK

It seems an obvious approach to me that if you're given a statement "there exists ..." and you're told not to use the $\exists$ symbol, then the first step is to rephrase the statement to avoid the phrase "there exists". That, it seems to me, is logical!

As a start, you could think of a statement like "not all primes are odd". This starts to take you in the right direction, I believe.