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Universal Quantifier question

  • Thread starter mattmns
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I have a question that says, determine the truth value of: [tex]\exists x \ni \forall y, \exists z \ni xz = y[/tex]

I am thinking this is false because: If you let x = 0, and let y = 1, then there is no value of z that will make the statement true. Am I thinking about this correctly?
 

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Your reasoning would be right if that was a universal quantifier instead of an existential one. All you have to find is one x where this is true and the statement is true.
 
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So if x=1 then for every value of y there is a value of z such that xz = y.

So it is dependent on the statements afterward, the exestential quantifier [tex]\exists x[/tex] ? So I would say. There is a value of x such that for any value of y there is a value of z such that xz = y. I guess you are right, it sounds as though it depends on the things that follow. Thanks.
 

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