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Read the two statements shown below.
If the weather is not cold, Meg will go swimming.
The weather is cold, or Meg will go swimming.
Create truth tables for the logical form of the two statements (not to be submitted). Use the truth tables to determine whether the two statements are logically equivalent. Justify your answer.
 one year ago
 one year ago
Read the two statements shown below. If the weather is not cold, Meg will go swimming. The weather is cold, or Meg will go swimming. Create truth tables for the logical form of the two statements (not to be submitted). Use the truth tables to determine whether the two statements are logically equivalent. Justify your answer.
 one year ago
 one year ago

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satellite73Best ResponseYou've already chosen the best response.0
they are equivalent, as the truth tables are the same to turn \(P\to Q\) into an equivalent or statement \[P\to Q\equiv \lnot P\lor Q\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
here is the truth table for \(P\to Q\) \[\begin{array}{ccc} P & Q & P\to{}Q \\ \hline T & T &T \\ T & F & F \\ F & T & T \\ F & F & T \\ \hline \end{array}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
and here it is for \(\lnot P\lor Q\) \[\begin{array}{cccc} P & Q & \lnot{}P & \lnot{}P\lor{}Q \\ \hline T & T & F & T \\ T & F & F & F \\ F & T & T & T \\ F & F & T & T \\ \hline \end{array}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
you can see that the last columns are identical, so it is equivalent
 one year ago

TurnerBest ResponseYou've already chosen the best response.0
Thanks you so much!! So if I wrote this in sentence form would this be correct These statements are equivalent, as their truth tables are the same. The P is true twice, and false twice for both statements, then the Q is T then F then T then F for both statements. The truth table column for P→Q is T, F, T, T as it is the same for ¬P∨Q.
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
yes although i would skip " The P is true twice, and false twice for both statements, then the Q is T then F then T then F for both statements." that is just how the truth table is constructed maybe put
 one year ago
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