Determine which, if any, of the three statements are equivalent. Give a reason f

Question

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

I) If tomorrow is not Monday, then today is not Sunday.
II) Today is not Sunday and tomorrow is not Monday.
III) It is not the case that today is Sunday and tomorrow is Monday.

a. I and II are equivalent
b. II and III are equivalent
c. I and III are equivalent
d. None are equivalent
e. I, II, and III are equivalent

Explanation / Answer

Let A: Tomorrow is Monday B: Today is Sunday Then I) not A -> not B II) (not B) and (not A) III) not B and A. Consider the truth table: A B I II III T T T F F T F T F T F T F F F F F T T F You can see that the last 3 columns, which correspond with I, II and III, are all different. Therefore the answer is d: None are equivalent These are equivalent forms for I and II: not A -> not B B -> A not B or A. (not B) and (not A) not (A or B) by De Morgan's Laws.

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