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# If a = true , b = false , c = true then (a and b and c) = ?

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If a = true , b = false , c = true then (a and b and c) = ?

Guest Jun 30, 2014

#8
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Here's my take on this.......

T ^ F ^ T  =

(T ^ F)  ^ T =

(F) ^ T  =

F

To verify this....here's is the truth table for a^b^c = p^q^r....the third row shows the result for  T^F^T

CPhill  Jun 30, 2014
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#1
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To me this question is nonsense but Alan already answered it anyway.

Added later: Boolean logic - yes I should have realised.

http://web2.0calc.com/questions/if-1-2-5-and-3-4-12-then-10-13

Melody  Jun 30, 2014
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This is a question of Boolean logic, where the logic table for AND looks like:

Alternatively, think of AND as multiply, true as 1 and false as 0.

Alan  Jun 30, 2014
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So it just means " A and B and C are all true."

And the answer is false ?

Melody  Jun 30, 2014
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No.  If you think of AND as "multiply", with "true" as 1, and "false" as 0; then

a=1, b=0, c=1 so (a and b and c) becomes 1*0*1 which is 0.

Since 0 represents false, then (a and b and c) = (true and false and true) = false.

Alan  Jun 30, 2014
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Thanks Alan but can you give an example of when my interpretation is wrong?

If they are not all true there will be a 0 on the mix. When multiplied the answer will be 0 so the answer will be false.

Melody  Jun 30, 2014
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Err.. Your post said "So it just means " A and B and C are all true." And the answer is false ?"

If you meant "So it just means " A and B and C are not all true." then, yes, the answer is false.  If they are all true the answer is true.

Alan  Jun 30, 2014
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No I meant that the statement is "A , B and C are all true."

And the statement is clearly false.

Melody  Jun 30, 2014
#8
+85644
+5

Here's my take on this.......

T ^ F ^ T  =

(T ^ F)  ^ T =

(F) ^ T  =

F

To verify this....here's is the truth table for a^b^c = p^q^r....the third row shows the result for  T^F^T

CPhill  Jun 30, 2014
#9
+26625
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Melody, I don't think the combination (a and b and c) should be read as "a and b and c are true" any more than the combination 1*0*1 should be read as "1*0*1 = 1".

However, I guess I'm still not understanding your meaning!

Alan  Jun 30, 2014
#10
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I am not saying that the statement is true  I am saying that it is a statement and the statement is false.

Like

Statement: All dogs have 5 legs and all cats are mammals.

This logic statement is FALSE

----------------------

In your example the  statement is 1*0*1=1 And this statement is FALSE.  I don't particlualy like the zero and one analogy but I can see that it also works.

Melody  Jul 1, 2014

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