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Kisachek [45]
3 years ago
11

Let A be the set of all lines in the plane. Define a relation R on A as follows. For every l1 and l2 in A, l1 R l2 ⇔ l1 is paral

lel to l2. (Assume that a line is parallel to itself). Which of the following is true for R?
A. R is reflexive.
B. R is symmetric.
C. R is transitive.
D. R is neither reflexive, symmetric, nor transitive.
Mathematics
1 answer:
Lyrx [107]3 years ago
7 0

Answer:

Hence, the relation R is a reflexive, symmetric and transitive relation.

Given :

A be the set of all lines in the plane and R is a relation on set A.

R=\{l_1,l_2\in A|l_1 \;\text{is parallel to}\; l_2\}

To find :

Which type of relation R on set A.

Explanation :

A relation R on a set A is called reflexive relation if every a\in A then (a,a)\in R.

So, the relation R is a reflexive relation because a line always parallels to itself.

A relation R on a set A is called Symmetric relation if (a,b)\in R then (b,a)\in R for all a,b\in A.

So, the relation R is a symmetric relation because if a line l_1 is parallel to the line l_2 the always the line l_2 is parallel to the line l_1.

A relation R on a set A is called transitive relation if (a,b)\in R and (b,c)\in R then (a,c)\in R for all a,b,c\in A.

So, the relation R is a transitive relation because if a line l_1 s parallel to the line l_2 and the line l_2 is parallel to the line l_3 then the always line l_1 is parallel to the line l_3.

Therefore the relation R is a reflexive, symmetric and transitive relation.

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