Universal Quantifier: Determining Truth Value in Existential Statements

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In summary, the conversation discusses determining the truth value of a statement with an existential quantifier. The participants consider different scenarios and come to the conclusion that the statement is dependent on the values that follow it.
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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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  • #2
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.
 
  • #3
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.
 

What is a universal quantifier question?

A universal quantifier question is a type of question that asks about all members of a specific group or category. It is used to make general statements or observations about a certain topic.

How is a universal quantifier question different from other types of questions?

Unlike other types of questions that focus on specific individuals or situations, a universal quantifier question looks at the bigger picture and considers all possible cases. It is a more general and abstract way of asking about something.

What are some examples of universal quantifier questions?

Some examples of universal quantifier questions include: "What causes climate change?", "How do animals communicate?", and "What are the effects of technology on society?". These questions all ask about a broad topic or concept rather than a specific instance.

How are universal quantifier questions used in scientific research?

Universal quantifier questions are commonly used in scientific research to explore and understand broad topics or phenomena. They can help researchers make generalizations and draw conclusions about a larger population or system.

What are the advantages and disadvantages of using universal quantifier questions?

The main advantage of using universal quantifier questions is that they allow for a broader understanding of a topic and can lead to new insights and discoveries. However, they can also be difficult to test and prove, as they often involve complex and abstract ideas. Additionally, they may overlook individual differences and nuances within a topic.

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