a Reflexive Explain why or why not b Symmetric Explain why o

(a) Reflexive? Explain why, or why not?

(b) Symmetric? Explain why, or why not?

(c) Transitive? Explain why, or why not?

(a) The relation is reflexive, because xRx if and only if, x+x>3 => 2x>3 => x>3/2 = 1.5 and this is true

(b) The relation is symmetric, because if xRy then yRx. This is because as x+y>3 then y+x>3

(c) Now if xRy and yRz then x+y>3 and y+z>3, then x+y+z>x+z>3+z>4

And so the relation R is not transitive as x is not related to z

For example, if z=1,y=3 and x=1 then x+y = 4>3 and also y+z =4 >3 but x+z = 2 <3 and hence x is not related to z