Question

Determine which, if any, of the three statements are equivalent.
I) If there is an opera performance, then Paula will not wear jeans.
II) If there is no opera performance, then Paula will wear jeans.
III) Either there is an opera performance or Paula will wear jeans.
(Points : 2)
I, II, and III are equivalent
I and II are equivalent
I and III are equivalent
II and III are equivalent
None are equivalent

Answer 1

p: there is an opera performance
q: Paula will wear jeans

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~p: there is an opera performance
~q: Paula will not wear jeans

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Statement I: If there is an opera performance, then Paula will not wear jeans. translates to p --> ~q

Statement II: If there is no opera performance, then Paula will wear jeans. translates to ~p --> q

Statement III: Either there is an opera performance or Paula will wear jeans. translates to p V q

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Truth table for each


Truth table for p --> ~q

p q ~q p --> ~q
----------------------------------
T T F F
T F T T
F T F T
F F T T




Truth table for ~p --> q

p q ~p ~p --> q
----------------------------------
T T F T
T F F T
F T T T
F F T F



Truth table for p V q

p q p V q
----------------------
T T T
T F T
F T T
F F F


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Now compare the last columns of the truth tables above.


We see that the last columns of the last two truth tables are identitical.


So ~p --> q is equivalent to p V q


So the answer is choice D) II and III are equivalent

Answer 2

i think it would be # 3

Answer 3

all three would be equivalent so the answer would be #1

Answer 4

no, the first one is not equivalent to the other two

Answer 5

look at the last column of each truth table

Answer 6

ok i see it now.. :)