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Can anyone explain this $P \rightarrow Q$ and how do we get true,false,true,true from the truth table in the third column? I know the first two colums but i am confused how to get the third row.can anyone help me I am really confused.

Furthermore, what is $P \leftrightarrow Q$?

naslundx
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nelson
  • 33

2 Answers2

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To construct the truth table, you will have to figure out if the statement is true or false given the values of $P$ and $Q$. We get the following:

  • If both $P$ and $Q$ are true, then $P\Rightarrow Q$ must also be true.
  • If $P$ and $Q$ are both false, then $P\Rightarrow Q$ is still true (to see this, imagine a politician saying: "If I am elected for President ($P$), then I will lower taxes ($Q$)". If he is not elected, you cannot say that he is lying, since he only stated his intentions if elected).
  • If $P$ is true, and $Q$ is false, then clearly $P\Rightarrow Q$ must be false (In the previous example, the politician would have told a lie).
  • If $P$ is false, and $Q$ is true, $P\Rightarrow Q$ would also be true. (Again, even if the politician was not elected, he could still work to lower taxes.)

Summarising this in the truth table, we get

P | Q | P -> Q
T   T     T
T   F     F
F   T     T
F   F     T
René B. Christensen
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0

there exist well know table for true table,which includes all basic operations(implication,negation, and so on)

enter image description here

also another table

enter image description here

look please there

http://c2.com/cgi/wiki?LogicalImplication

dato datuashvili
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