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Answer :
In terms of quantifiers, 'n is odd' means there exists an integer k such that n equals 2k + 1.
In terms of quantifiers, saying "n is odd" can be expressed using existential quantification in a logical statement. Specifically, a number n is odd if there exists an integer k such that n equals 2k + 1.
This can be written formally using existential quantifiers as follows: ∃k ∈ ℤ (n = 2k + 1), which reads as "There exists an integer k such that n equals 2k plus 1." This quantifier expression succinctly captures the property of n being odd.
Step-by-step explanation:
- Identify the definition: A number n is odd if it can be written as 2k + 1 where k is an integer.
- Translate to logical form: Use the existential quantifier (∃) to indicate the existence of an integer k.
- Formulate the statement: ∃k ∈ ℤ (n = 2k + 1).
- Interpret: This statement means there is some integer k for which the equation holds, implying n is odd.
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