I have been working on problems from Velleman's
How to Prove book and hit upon the following problem:
Translate the following statements into idiomatic mathematical English:
∃x[P(x) ∧ ∀y(P(y) → y ≤ x)], where P(x) means “x is a perfect number.”
I worked out the problem in the following steps:
* ∃x[P(x) ∧ ∀y(P(y) → y ≤ x)] * ∃x(P(x) ∧ ∀y(If y is a perfect number then y is less than or equal to x.)) * ∃x(P(x) ∧ Every perfect number is less than or equal to x.) * Every perfect number is less than or equal to some perfect number.
But the idiomatic answer seems to be:
There exists a perfect number such that all the other perfect numbers are either less or equal to it.
I would like to know if there is any problem with my solution ? Also, I would like to know if there are some general guidelines while forming the idiomatic mathematics statement (or any statement) from logical connectives.