Tricky Logical Problem: Solving for \forallx\forally\existsz

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In summary, a tricky logical problem requires a deep understanding of logic and critical thinking skills to solve. It involves complex equations or statements that can be logically deduced to find a solution. The symbols \forallx\forally\existsz represent a logical statement involving universal and existential quantifiers. The process for solving a tricky logical problem involves breaking down the problem, identifying given information, and using logical reasoning and deduction. Some strategies for solving these problems include breaking them down, using logical rules, and practicing logical thinking. Solving these problems is important for developing critical thinking skills, efficient problem-solving, and intellectual stimulation.
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Homework Statement


This is a problem I have been had some troubles understanding in my Discrete Mathematics course.

[PLAIN]http://i.imgur.com/HTUNr7f.png[/PLAIN]


[itex]\forall[/itex]x[itex]\forall[/itex]y[itex]\exists[/itex]z(x<z[itex]\rightarrow[/itex]x≥y)



Homework Equations



I know that this statement is true, according to the solutions page, but I just cannot comprehend why?



The Attempt at a Solution



Does anyone have any ideas?
 

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The statement is true, because if you choose z to be less or equal to x, then (x < z) is a false statement, so (x < z ) -> A is always true, regardless of "A".
 

What is a tricky logical problem?

A tricky logical problem is a problem that requires a deep understanding of logic and critical thinking skills to solve. It often involves complex equations or statements that may seem confusing at first, but can be logically deduced to find a solution.

What is the meaning of \forallx\forally\existsz?

The symbols \forallx\forally\existsz are part of a mathematical notation called first-order logic. \forallx means "for all x," \forally means "for all y," and \existsz means "there exists a z." Together, they represent a logical statement that involves universal and existential quantifiers.

What is the process for solving a tricky logical problem?

The process for solving a tricky logical problem involves breaking down the problem into smaller, more manageable parts, identifying any given information or constraints, and using logical reasoning and deduction to arrive at a solution. It may also involve creating diagrams or tables to organize the information and make connections between different elements of the problem.

What are some strategies for solving tricky logical problems?

Some strategies for solving tricky logical problems include breaking down the problem into smaller parts, using logical rules and principles to make deductions, identifying any given information or constraints, and checking the validity of each step in the solution. It can also be helpful to practice and strengthen logical thinking skills through puzzles and exercises.

Why is solving tricky logical problems important?

Solving tricky logical problems helps to develop critical thinking skills, which are essential in many fields such as science, mathematics, and computer science. It also allows for more efficient problem-solving in everyday life, as well as in more complex and technical situations. Additionally, solving tricky logical problems can be intellectually stimulating and enjoyable.

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