Negating the statement: \exists M \in R such that \forall x\in S, x\leqM

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In summary, the negation of a statement is the opposite or denial of the original statement, typically represented by "~" or "¬". It is important in scientific research as it allows for consideration of alternative explanations and avoidance of bias. In logic, it is symbolized using "~" or "¬" before the statement. It differs from a contrapositive, which involves switching the subject and predicate and negating both. Negation of statement cannot be used to prove a statement is true, as it only shows the opposite is false.
  • #1
brntspawn
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Homework Statement



[tex]\exists[/tex] M [tex]\in[/tex] R such that [tex]\forall[/tex] x[tex]\in[/tex] S, x[tex]\leq[/tex]M
Write in symbolic for the negation of the statement.

The Attempt at a Solution


[tex]\forall[/tex] M[tex]\in[/tex] R, [tex]\exists[/tex] x[tex]\in[/tex] S such that x[tex]\geq[/tex]M

Is this correct?
 
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  • #2
It should be x > M, but otherwise yes.
 
  • #3
Great. Thanks for the help.
 

FAQ: Negating the statement: \exists M \in R such that \forall x\in S, x\leqM

What is the definition of "negation of statement"?

The negation of a statement is the opposite or denial of the original statement. It is typically represented by the symbol "~" or "¬".

Why is negation of statement important in scientific research?

Negation of statement allows scientists to consider alternative explanations or hypotheses and evaluate their validity. It also helps to avoid bias and ensure that all possible outcomes are considered.

How do you symbolize negation of statement in logic?

The negation of a statement can be symbolized using the tilde "~" or "¬" before the statement. For example, the negation of the statement "All mammals have fur" would be "~(All mammals have fur)" or "¬(All mammals have fur)".

What is the difference between negation of statement and contrapositive?

Negation of statement simply flips the truth value of the original statement, while contrapositive involves switching the subject and predicate and negating both. For example, the negation of "If it is raining, then the ground is wet" would be "It is not the case that if it is raining, then the ground is wet." The contrapositive would be "If the ground is not wet, then it is not raining."

Can negation of statement be used to prove a statement is true?

No, negation of statement only shows that the opposite of the original statement is false. In order to prove a statement is true, it must be supported by evidence and logical reasoning.

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