What Math Is This? (Logic of Mathematics)

In summary: It isn't true that P(x) is true for all x ≡ not all x have a value of "true".There is a quantifier in each of the first three lines, but they're not really doing anything with them. I suppose the first line means that:~(∀x : P(x) ) ≡ Ex: ~(P(x)) which meansIt isn't true that P(x) is true for all x ≡ not all x have a value of "true".In summary, this is a picture of a math equation with incorrect statements. Symbolic Logic is involved, as is the use of quantifiers.
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Can someone please tell me what math is this (see below pic)? For example: algebra, calculus, etc.
 

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  • #3
Does the Truth Table is included in Symbolic Logic?
 
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Truth tables are an important basic tool of logic. But once some basic symbolic logic has been established (often using truth tables), it is easier to manipulate the symbols without resorting to truth tables.
 
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askor said:
Can someone please tell me what math is this (see below pic)?
Note that some of the statements in the picture are incorrect.
 
  • #7
I'd say this is Sentence Logic, as the inner structure of sentences is not considered, but rather it only matters whether they're assigned one of the values T or F.
 
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askor said:
Can someone please tell me what math is this (see below pic)? For example: algebra, calculus, etc.
pbuk said:
Note that some of the statements in the picture are incorrect.
Rhut-rho. @askor -- Please always post links to where you get images and quotes, etc. Where did you get this?
 
  • #9
My bad. I think I was only partially right, given the quantifies. It seems like a mix of Sentence Logic and Symbolic/First Order Logic. My bad.
 
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WWGD said:
My bad. I think I was only partially right, given the quantifies. It seems like a mix of Sentence Logic and Symbolic/First Order Logic. My bad.
Their use of quantifiers is weird. In all but the first two lines, p and q are logic propositions, which might be true or false, but ∀p or ∃p, really doesn't make sense make by itself. I suppose the first line means that:
~(∀x : P(x) ) ≡ Ex: ~(P(x)) which means
It isn't true that P(x) is true for all x is equivalent to there exists an x for which P(x) is false.
P(x) is a proposition that depends on x, such as x is married. This means the same as: if not everyone is married, there must exist an unmarried person.
 
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