# If and only if relationship between them?

1. Apr 23, 2010

### _DJ_british_?

"if and only if" relationship between them?

Hi Pfers, just a little question :

If you have a problem of the form "Show that these definitions are equivalent",do I basically have to prove an "if and only if" relationship between them?

2. Apr 23, 2010

### Neveos

Re: Equivalence

Equivalence is different from identity in math, in that, if two sides of an equation are equivalent, as opposed to identical, it just means that there are variables involved of which there are only certain values (in place of the variable(s)) that make the equation a case of identity. So, 3+3 = 6 is a case of identity, while 3 + x = 6 is a case of equivalence, since there is a variable involved (to put it simply). x * 0 = 6 is a case of non-equivalence, since both sides of the equation can never be identical.

You seem to be talking about logic, though (and answering a question), so, yes, you'll want to show that an "if and only if" is possible.