Let R be a relation on the set of all lines in a plane defined by (l 1 , l 2 ) R line l 1 is parallel to l 2 . Show that R is an equivale

Question

Let R be a relation on the set of all lines in a plane defined by (l 1 , l 2 ) R line l 1 is parallel to l 2 . Show that R is an equivalence relation.

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Thu Nguyệt 6 months 2021-07-17T12:34:25+00:00 1 Answers 5 views 0

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    2021-07-17T12:36:12+00:00

    Answer: hello your question is poorly written below is the complete question

    Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2): L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.

    answer:

    a ) R is equivalence

    b) y = 2x + C

    Step-by-step explanation:

    a) Prove that R is an equivalence relation

    Every line is seen to be parallel to itself ( i.e. reflexive ) also

    L1 is parallel to L2 and L2 is as well parallel to L1 ( i.e. symmetric ) also

    If we presume L1 is parallel to L2 and L2 is also parallel to L3 hence we can also conclude that L1 is parallel to L3 as well ( i.e. transitive )

    with these conditions we can conclude that ; R is equivalence

    b) show the set of all lines related to y = 2x + 4

    The set of all line that is related to y = 2x + 4

    y = 2x + C

    because parallel lines have the same slopes.

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