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Question
Let L be a set of all straight lines in a plane. The relation R on L defined as 'perpendicular to' is ______.
Options
Symmetric and Transitive
Transitive
Symmetric
Equivalence
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Solution
Let L be a set of all straight lines in a plane. The relation R on L defined as 'perpendicular to' is symmetric.
Explanation:
The relation is symmetric, meaning that if a line (I) is perpendicular to line (m), then line (m) is also perpendicular to line I.
However, if line (l) is perpendicular to line (m) and line (m) is perpendicular to line (n).
Then, lines 'I' and 'n' are parallel rather than perpendicular, but is parallel.
As a result, the provided relation is only symmetric.
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