Question

MULTIPLE SELECT QUESTIONS:
7) Let X be the set of all straight lines in the coordinate plane. Let us define a relation 1 point
Ron X as follows, R := {(li,l2) E X X X | The lines l¡ and la intersect at least at one
point}.Which of the following statements is/are true?
R is symmetric.
R is transitive.
Ris reflexive.
R is an equivalence relation.
8) Consider three​

Answer 1

Step-by-step explanation:

I think this

is mathematics

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTIONS

Let X be the set of all straight lines in the coordinate plane. Let us define a relation R on X as follows,

R = { (l1 ,l2) X × X | The lines l1 and l2 intersect at least at one point}.

Which of the following statements is/are true?

• R is symmetric.

• R is transitive.

• Ris reflexive.

• R is an equivalence relation.

EVALUATION

Here it is given that

Let X be the set of all straight lines in the coordinate plane. Let us define a relation R on X as follows,

R = { (l1 ,l2) X × X | The lines l1 and l2 intersect at least at one point}.

CHECKING FOR REFLEXIVE

Let L ∈ X

Since a line cannot intersect itself

So (L, L) ∉ R

So R is not Reflexive

CHECKING FOR SYMMETRIC

Let L , M ∈ X and (L, M) ∈ R

Now (L, M) ∈ R

⇒ L and M at least at one point

⇒ M and L at least at one point

⇒(M, L) ∈ R

Thus (L, M) ∈ R implies (M, L) ∈ R

So R is symmetric

CHECKING FOR TRANSITIVE

Let L , M , N ∈ X

Also let (L, M) ∈ R and (M, N) ∈ R

Now (L, M) ∈ R and (M, N) ∈ R

⇒ L , M at least at one point and M , N at least at one point

Which does not imply L and N intersect ( Refer to the attachment )

In the attachment L , M at least at one point and M , N at least at one point but L , N does not intersect

⇒(L, N) ∉ R

So R is not transitive

FINAL ANSWER

Hence the correct option is

R is symmetric

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