Math homework: Equivalent Statements?
PLEASE SHOW SUPPORTIVE EVIDENCE b/c I'M TRYING TO SEE HOW TO WORK THRU THESE! THANKS IN ADVANCE!!! :)
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
- Anonymous9 years agoBest Answer
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.