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(a) How many elements are there in S/ ~ ? Equivalently, how man equivalence classes are there in S? (b) Write down the equivalence class containing 6. This should be subset of S

(a) How many elements are there in S/ ~ ? Equivalently, how man equivalence classes are there in S? (b) Write down the equivalence class containing 6. This should be subset of S

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Let \( S = \{1, 2, 3, 4, \ldots, 15\} \). For \( m, n \in S \), we say \( m \sim n \) if \( m, n \) have the same number of prime factors. For example, \( 3 \sim 4 \) because they both only have 1 prime factor, namely 3 and 2. This is an equivalence relation (which can be proved by Q1). (a) How many elements are there in \( S / \sim \)? Equivalently, how many equivalence classes are there in \( S \)? (b) Write down the equivalence class containing 6. This should be a subset of \( S \).
Transcribed Image Text:3. Let \( S = \{1, 2, 3, 4, \ldots, 15\} \). For \( m, n \in S \), we say \( m \sim n \) if \( m, n \) have the same number of prime factors. For example, \( 3 \sim 4 \) because they both only have 1 prime factor, namely 3 and 2. This is an equivalence relation (which can be proved by Q1). (a) How many elements are there in \( S / \sim \)? Equivalently, how many equivalence classes are there in \( S \)? (b) Write down the equivalence class containing 6. This should be a subset of \( S \).
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