Question

show that the relation r in the set r of real numbers defined by R={x,y]: x,y not belongs to Q, x

Answer 1

Step-by-step explanation:

R={(a,b):a≤b

2

}

It can be observed that (

2

1

,

2

1

)∈

/

R, since

2

1

>(

2

1

)

2

=

4

1

.

∴R is not reflexive.

Now, (1,4)∈R as 1<4

2

But, 4 is not less than 1

2

.

∴(4,1)∈

/

R

∴R is not symmetric.

Now, (3,2),(2,1.5)∈R

(as3<2

2

=4and2<(1.5)

2

=2.25)

But, 3>(1.5)

2

=2.25

∴(3,1.5)∈

/

R

∴R is not transitive.

Hence, R is neither reflexive, nor symmetric, nor transitive.