? asked in Science & MathematicsMathematics · 9 years ago

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

Relevance
  • Anonymous
    9 years ago
    Best 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.

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