Solve Logic Puzzle: Predicates & True/False Explained

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In summary, the conversation discusses the concepts of predicate and true/false statements. A predicate is a statement with unbound variables, and its negation can be either true or false. The first statement given, "Predicate. Negation is ¬(∃n ∈ N n²>n)", is false since its negation, "∃n ∈ N n²≤n", is true. The second statement, "True. Negation is, "When x<0 there is y such that y^2=x", is a predicate and its negation can be written as "∀x ∈ R if x<0 then ¬∃y ∈ R y^2=x". The third statement, "No clue :P
  • #1
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I'm unsure about these three, here are my attempts. Please also explain the difference between a predicate and true/false. I assumed it is a predicate when it can be either true or false.

a) Predicate. Negation is ¬(∃n ∈ N n²>n)
b) True. Negation is, "When x<0 there is y such that y^2=x
c) No clue :P

Your help is truly appreciated!
 

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  • #2
I assume by predicate, it is meant that the sentence has unbound variables. So

a) This is a statement. The negation is
$$\exists n \text{ such that }n\in N \text{ and }n^2\leq n$$
The negation is true (set n=1) and so the original statement is false.

b) The variable x is not bound, so this is a predicate. To make a statement one might say:
$$\forall x \in R\text{ if }x<0 \text{ then }\not\exists y\in R \text{ such that }y^2=x$$
I leave it to you to negate this statement.

c) This is a true statement. ("famous" theorem of Fermat says a prime is the sum of two squares iff the prime is congruent to 1 mod 4)
The negation is:
$$\exists p\in P \text{ such that }\exists n\in N \text{ with }p=4n+1\text{ and }\forall a\in N\,\forall b\in N\,a^2+b^2\neq p$$
 

FAQ: Solve Logic Puzzle: Predicates & True/False Explained

1. What is a logic puzzle?

A logic puzzle is a type of brainteaser that requires critical thinking and deductive reasoning to solve. It typically involves a set of clues or statements that must be analyzed in order to determine a solution or answer.

2. What are predicates in logic puzzles?

Predicates in logic puzzles are statements that describe a relationship or characteristic of the elements or variables in the puzzle. They can be used to narrow down possibilities and eliminate incorrect solutions.

3. How do you solve a logic puzzle?

To solve a logic puzzle, start by reading all of the clues carefully and identifying any predicates or key words. Then, use deductive reasoning and process of elimination to make logical deductions and eliminate incorrect possibilities. Continue to analyze the clues and make deductions until a single solution or answer is reached.

4. What is the difference between true and false statements in logic puzzles?

True statements in logic puzzles are those that are confirmed by the given clues and are necessary for the solution to be correct. False statements, on the other hand, are those that contradict the clues and cannot be true in the solution.

5. Are there any tips for solving logic puzzles?

Some tips for solving logic puzzles include looking for similar clues or patterns, making a grid or chart to organize information, and using the process of elimination to eliminate incorrect possibilities. It can also be helpful to start with the clues that provide the most information or are the most specific. Practice and patience are key when it comes to solving logic puzzles.

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