# Math homework: Equivalent Statements?

PLEASE SHOW SUPPORTIVE EVIDENCE b/c I'M TRYING TO SEE HOW TO WORK THRU THESE! THANKS IN ADVANCE!!! :)

Equivalent Statements?

Determine which, if any, of the three statements are equivalent. Give a reason for your conclusion. Show complete work and submit your solution

I) Gasoline costs $1.99 per gallon if and only if you live in Orange County.

II) You do not live in Orange County and gasoline does not cost $1.99 per gallon.

III) If you do not live in Orange County then gasoline does not cost $1.99 per gallon.

a. I, II, and III are equivalent

b. I and II are equivalent

c. II and III are equivalent

d. I and III are equivalent

e. None are equivalent

### 1 Answer

- Anonymous9 years agoBest Answer
Let's define:

p = "Gasoline costs $1.99 per gallon"

q = "You live in Orange County"

(I) p if and only if q

(II) (not q) and (not p)

(III) if (not q) then (not p)

None of these are equivalent statements.

(III) is equivalent to "if p then q" but that's only half of what (I) says.

(II) is not even close to the others.