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प्रश्न
Statement 1: If a relation R on a set A satisfies R = R–1, then R is symmetric.
Statement 2: For a relation R to be symmetric, it is necessary that R = R–1.
Which one of the following is correct?
पर्याय
Statement 1 is true and Statement 2 is false.
Statement 2 is true and Statement 1 is false.
Both the statements are true.
Both the statements are false.
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उत्तर
Both the statements are true.
Explanation:
Statement 1: A relation R is defined as symmetric if, whenever an ordered pair (a, b) is in R, the reverse ordered pair (b, a) is also in R.
The inverse relation R–1 is the set of all reversed pairs of R.
Therefore, if R = R–1, it means every element in R has its reverse in R, satisfying the definition of a symmetric relation.
Statement 2: This statement is the definition of a symmetric relation expressed in terms of the inverse relation.
For a relation to be symmetric, it is necessary that the set of ordered pairs in the relation (R) be identical to the set of ordered pairs in its inverse (R–1).
