Question

Determine which property(s) the following relation R on the set of all integers satisfy(s)?

( a , b ) ∈ R iff a b ≥ 1 .

Answer 1

Answer:-

The above set S={(1,1)(1,2)(2,1)..................}

It is an infinite set.

This set is reflexive because (i,i) is there if i>=1.

This set is symmetric because (i,j) and (j,i) is present in the set if i,j>=1.

This set is also transitive because (i,j) , (j,k) is there and (i,k) is also there because from (i,j) and (j,k) we can see that i,j,k>=1 so (i,k) is also possible.

So the relation is an equivalence relation as it is reflexive,symmetric and transitive.

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