Question

For the relation \(aRb\) defined by \(a-b<5\), which example shows that the relation is not transitive?

पर्याय

• \(a=2,b=8\): \(aRb\), but \(b\not Ra\)

• \(a=4,b=0,c=-4\): \(aRb\) and \(bRc\), but \(a\not Rc\)

• \(a=4,b=0,c=-4\): \(aRc\) because \(4-(-4)=8<5\)

• For every \(a\), \(aRa\) because \(a-a=0<5\)

Answer 1

Here, \(4-0=4<5\), so \(aRb\), and \(0-(-4)=4<5\), so \(bRc\). But \(4-(-4)=8\nless5\), so \(a\not Rc\), disproving transitivity.