Find the number of integers n such that 1 <= n <= 1000 and n is a multiple of 7 but not a multiple of 2 or 3.

May 28, 2026Mathematics

ScanSolve AI Answer

May 28, 2026

Answer

{1, 2, \dots, 1000}$.

The problem asks us to find the number of integers $n$ such that $1 \le n \le 1000$ and $n$ is a multiple of $7$ but not a multiple of $2$ or $3$ .

Let $S = \{1, 2, \dots, 1000\}$ . Let $A$ be the set of integers in $S$ that are multiples of $7$ . Let $B$ be the set of integers in $S$ that are multiples of $2$ . Let $C$ be the set of integers in $S$ that are multiples of $3$ .

We are looking for the number of integers $n$ such that $n \in A$ and $n \notin B$ and $

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The problem asks us to find the number of integers n such that 1 n 1000 and n is a multiple of 7 but not a multiple of 2 or 3.

Asked on May 28, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 28, 2026

The problem asks us to find the number of integers n such that 1 n 1000 and n is a multiple of 7 but not a multiple of 2 or 3. Let S = \1, 2, , 1000\. Let A be the set of integers in S that are multiples of 7. Let B be the set of integers in S that are multiples of 2. Let C be the set of integers in S that are multiples of 3. We are looking for the number of integers n such that n A and n B and $