How to assign truth value to the subset symbol? Watch

andrewk
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#1
Report Thread starter 10 years ago
#1
e.g.

Code:
A  B  C:   A \cup B \subset C
I   I    I        I
I   I   O        I
I   O   I        I
I   O  O        I
O  I    I        I
O  I   O        I
O  O   I        O
O  O  O        O
But i don't when to put an I or O for the subset part?
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Dadeyemi
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Report 10 years ago
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hmm, doesn't really apply to truth tables, only sets. If you consider 0 to be the null set and 1 = {1} then you could do it.
(A \subset B ) \Leftrightarrow  \lnot A
which is for proper subsets like you have used in your notation.

Or...
(A \subseteq B ) \Leftrightarrow  B \lor \lnot A
which is for subsets like I think you meant.

Or you could consider true and false to be mutually exclusive so
(A \subseteq B ) \Leftrightarrow  (\lnot B \land \lnot A) \lor (B \land A)

I think these work in a way but generally speaking subset doesn't really make sense when applied to logic.
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Kolya
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Report 10 years ago
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To assign a truth value to subset, recall that A \subseteq B \Leftrightarrow A\cap ¬B = \emptyset Thus the truth table for \subseteq is:

A\subseteq B
T F T
T F F
F T T
F F F

At least, this definition seems to make sense.
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