1. Feb 2, 2009

### Swimdownhill

1. I am a 47 year old man returning to school after so many years. I really need helpwith my Math. I am working on another degree and I have forgot everything in math.

Here is the problem

Let p be “The object belongs to set A.” Let q be
“the object belongs to set B.”
All A is B is equivalent to p →q.
No A is B is equivalent to p →∼q.
Some A is B is equivalent to p ∧ q.
Some A is not B is equivalent to p ∧∼q

Paul Murphy

3. The attempt at a solution

2. Feb 2, 2009

### Swimdownhill

Truth tables are related to Euler circles. Arguments in
the form of Euler circles can be translated into statements
using the basic connectives and the negation as follows:
Let p be “The object belongs to set A.” Let q be
“the object belongs to set B.”
All A is B is equivalent to p →q.
No A is B is equivalent to p →∼q.
Some A is B is equivalent to p ∧ q.
Some A is not B is equivalent to p ∧∼q.
Determine the validity of the next arguments by
using Euler circles, then translate the statements into
logical statements using the basic connectives, and
using truth tables, determine the validity of the