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corpsia
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$7.00 Quantitifier and predicate 2...

• From Mathematics: Discrete-Mathematics , Mathematics: Logic
• Closed, but you can still post tutorials
• Due on Nov. 09, 2009
• Asked on Nov 06, 2009 at 6:27:30PM

Q:

 

Problem 1

Write the following sentence in a formalised language (langage formalise) with these symbols (it will be letters because i don’t want to bother you

A for the addition

B for the multiplication

C for the inequation

D for the equality

0 for zero

a)      It exists two different numbers who has the same square ( equal)

b)      For each number there exist his own negative

c)       Each positive number has the square ( i mean exposant 2)  as definite positive number

 

Problem 2

 

We consider in formalised language with this symbol B for the multiplication, c for the inequation and 0 for 0.  This sentence:

 

∃x ∀y (( y B y) B y C x)

 

Is valid

a)    For the model M₁= (Q,0, . , =) ?

b)    For the model M₂=(R,0, . , =) ?

 

Justify

Q is the set of rational number

R is the set of real number

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Attachments:
devoir_7.pdf (27K)

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