00:01
Hello students, let's discuss the question.
00:03
Here, relation on the set of positive integer is given as r is equal to x -coma -y such that x is greater than or equal to 3 -y.
00:15
Now, if x -coma -x belongs to r, then it should fulfill this condition, that is, x should be greater than or equal to 3x this condition can this is not possible so we can write that x comma x does not belongs to r which implies that r is not reflexive proceeding next it is given that if x comma y belongs to r then this implies x is greater than or equal to three one now if we reverse the order of x and y that is y comma x if we want to check whether this belongs to this then it should follow it should fulfill the condition that is y should be greater than or equal to three now this inequality and this inequality cannot be satisfied simultaneously.
01:48
Suppose we want to check 3 comma 1 then 3 is greater than equal to 1 multiplied by 3.
02:03
This gives 3 is greater than or equal to 3.
02:07
This satisfied the inequality.
02:09
But if we reverse the ordered pair 1 comma 3 then 1 greater than equal to 3 multiplied by 3 this does not satisfy the inequality so y comma x does not belong to r this implies that r is not symmetric now let x x.
02:51
Y belongs to r such that x is greater than and equal to three y and y comma z also belongs to r such that y is greater than equal to three z.
03:12
Now x is greater than equal to three y and y is greater than equal to three z.
03:22
So combining we'll get x greater than or equal to putting the value of y from this inequality we'll get 3 z...