Question

For , ∈ ℝ define to mean that | − | < 5.
please help me​

Answer 1

Answer:

A={1,2,3,5} and B={4,6,9}

R={(x,y): the difference between x and y is odd x∈A,y∈B}

∴R={(1,4),(1,6),(2,9),(3,4),(3,6),(5,4),(5,6)}

Step-by-step explanation:

Answer 2

Answer: 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.