Mathematics
Assertion (A): Two ordered pairs (a, b) and (c, d) are equal if a = c and b = d.
Reason (R): If a ≠ b, then (a, b) ≠ (b, a).
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Coordinate Geometry
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Answer
Two ordered pairs (a, b) and (c, d) are equal if a = c and b = d.
This statement is the definition of equality for ordered pairs. For two ordered pairs to be considered equal, their corresponding elements must be equal.
So, (a, b) = (c, d) if and only if a = c and b = d.
∴ Assertion (A) is true.
If a ≠ b, then (a, b) ≠ (b, a).
For example, the ordered pair (2, 3) is not the same as (3,2). They represent different points in a coordinate plane.
∴ Reason (R) is true.
∴ Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Hence, option 4 is the correct option.
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