Question

Why is the “is greater than” relation on \(A=\{2,4,6,8\}\) not symmetric?

पर्याय

• If \(x>y\) and \(y>z\), then \(x>z\)

• \((2,2)\notin R\)

• \((8,6)\in R\) and \((6,8)\in R\)

• \((8,6)\in R\) but \((6,8)\notin R\)

Answer 1

Symmetry would require that \((8,6)\in R\) imply \((6,8)\in R\). Since \(8>6\) but \(6>8\) is false, the relation is not symmetric.