Math Problem Statement
- The contrapositive of ”If x∈N,then x is integer and x>0"is-----------------------------------------------------------------------------------------------------------------------------------------
Solution
The contrapositive of the statement "If , then is an integer and " is:
"If is not an integer or , then ."
Explanation:
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The original statement is of the form "If , then ," where:
- : (x belongs to the set of natural numbers)
- : is an integer and
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The contrapositive of "If , then " is "If not , then not ."
- Not : is not an integer or
- Not : (x does not belong to the set of natural numbers)
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Further Questions:
- What is the difference between the contrapositive, converse, and inverse of a statement?
- How do you prove that the contrapositive of a statement is logically equivalent to the original statement?
- What are some examples of contrapositive statements in real-life scenarios?
- How does the concept of contrapositive help in mathematical proofs, especially in proving implications?
- Can you explain the role of contrapositive in logical reasoning and decision-making processes?
Tip:
When constructing the contrapositive, remember that you negate both parts of the statement and reverse the direction of the implication.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Logical Implications
Formulas
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Theorems
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Suitable Grade Level
College Level
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