2. Consider the relation p- on natural numbers relating numbers that nave tne same number of prime factors. For example, 2-p=3 and 6-p-10, while 6rp 3 and órpr12 (I use the symbol rpr to denote elements that are not related.) Is -p= reflexive? Is =p= symmetric? Is -p= anti-symmetric? Is -p- transitive? Give reasons!

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. Consider the relation -p= on natural numbers relating numbers that nave tne same number of prime factors. For example, 2=p=3 and 6-p=10, while 6*p+3 and 6*pr12 (I use the symbol pe to denote elements that
are not related.) Is =p= reflexive? Is =p= symmetric? Is =p= anti-symmetric? Is =p= transitive? Give reasons!
Transcribed Image Text:2. Consider the relation -p= on natural numbers relating numbers that nave tne same number of prime factors. For example, 2=p=3 and 6-p=10, while 6*p+3 and 6*pr12 (I use the symbol pe to denote elements that are not related.) Is =p= reflexive? Is =p= symmetric? Is =p= anti-symmetric? Is =p= transitive? Give reasons!
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