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Let L denote the set of all straight lines in a plane. Let a relation R be l R m if l is perpendicular to m ∀ l, m ∈ L. Then R is:
- a)reflexive
- b)symmetric
- c)transitive
- d)equivalence
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Let L denote the set of all straight lines in a plane. Let a relation ...
Let two lines ℓ1, ℓ2 ∈ L
Now (ℓ1, ℓ2) ∈ R
Only when ℓ1 ⊥ ℓ2
1. For reflexivity:
Let ℓ1 ∈ L
But (ℓ1, ℓ1) ∉ R
Since no line is perpendicular to itself
R is not reflexive
Now (ℓ1, ℓ2) ∈ R
Only when ℓ1 ⊥ ℓ2
1. For reflexivity:
Let ℓ1 ∈ L
But (ℓ1, ℓ1) ∉ R
Since no line is perpendicular to itself
R is not reflexive
2. For symmetric:
Let, (ℓ1, ℓ2) ∈ L
Now, if ℓ1 ⊥ ℓ2 then this implies that ℓ2 is also perpendicular to ℓ1
Hence, (ℓ1, ℓ1) ∈ L
R is symmetric.
Let, (ℓ1, ℓ2) ∈ L
Now, if ℓ1 ⊥ ℓ2 then this implies that ℓ2 is also perpendicular to ℓ1
Hence, (ℓ1, ℓ1) ∈ L
R is symmetric.
3. For Transitive:
Let (ℓ1, ℓ2) ∈ L and (ℓ2, ℓ3) ∈ L
ℓ1 ⊥ ℓ2 and ℓ2 ⊥ ℓ3
Let (ℓ1, ℓ2) ∈ L and (ℓ2, ℓ3) ∈ L
ℓ1 ⊥ ℓ2 and ℓ2 ⊥ ℓ3
ℓ1 is not perpendicular to ℓ3
(ℓ1, ℓ3) ∉ R
∴ Not transitive
(ℓ1, ℓ3) ∉ R
∴ Not transitive
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Community Answer
Let L denote the set of all straight lines in a plane. Let a relation ...
The relation R can be defined as follows:
R = {(l, m) | l is perpendicular to m}
In other words, the relation R consists of ordered pairs (l, m) where l and m are straight lines in the plane, and l is perpendicular to m.
R = {(l, m) | l is perpendicular to m}
In other words, the relation R consists of ordered pairs (l, m) where l and m are straight lines in the plane, and l is perpendicular to m.
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Let L denote the set of all straight lines in a plane. Let a relation R be l R m if l is perpendicular to m ∀ l, m ∈ L. Then R is:a)reflexiveb)symmetricc)transitived)equivalenceCorrect answer is option 'B'. Can you explain this answer?
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