# Nested Quantifiers

• Feb 23rd 2009, 08:36 AM
smartguy
Nested Quantifiers
need help with this

Use (nested) quantifiers and predicates to express the following statements.

a) “There is someone in class who on every day of 2007 drank coke.”

b) “There isn't any person in the room who has visited every capital city in world.”

c) “For each real number, there is another number which is its additive inverse.”
• Feb 23rd 2009, 04:41 PM
benes
Quote:

Originally Posted by smartguy
need help with this

Use (nested) quantifiers and predicates to express the following statements.

a) “There is someone in class who on every day of 2007 drank coke.”

b) “There isn't any person in the room who has visited every capital city in world.”

c) “For each real number, there is another number which is its additive inverse.”

As i said in another thread a good book with a lot of examples in formalizing every day sentences is: Logic by schaum's outline series

Problem (c) in your question is a classic formalization of the additive inverse in real Nos

Here formalization can be done in two ways:

1) If you mention the set in which you state your axioms and definitions,which in this case in concern is the set of real Nos,then we have:

$\forall x\exists y. x+y=0$

2) if you do not define the set then you can include it in your formalization in the following way:

$\forall . x\in R\rightarrow\exists y (y\in R\wedge x+y=0)$

YOU can do the rest of the problems