Question

12. An integer m is said to be related to another integer n if m is a multiple of n. Check if the
relation is symmetric, reflexive and transitive.
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Answer 1

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Answer 2

Answer:

Let us denote this relation by R and R={(m,n):m is a multiple of n with m,n∈Z}.

Then this relation is reflexive as every integer is a multiple of its own i.e. (a,a)∈R, ∀a∈Z ( set of integers).

Again this relation is not symmetric since 4 is a multiple of 2 but 2 is not a multiple of 4 i.e. (4,2)∈R but (2,4)

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∈R.

Also this relation is transitive as if a is a multiple of b and b is a multiple of c then naturally a is a multiple of c i.e. (a,b)∈R,(b,c)∈R⇒(a,c)∈R, ∀a,b,c∈Z.

So this relation is transitive.

Step-by-step explanation:

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