Given below are two statements:
One is labelled as Assertion A and the other is labelled as Reason R . Assertion A: If \( a \neq b \) , then \( (a, b) \neq(b, a) \) Reason R. (4,-3) lies in quadrant IV. In the light of the above statements, choose the correct answer from the options given belowLet's analyze both statements:
- Assertion A: If \( a \neq b \), then \( (a, b) \neq (b, a) \).
- This is true because an ordered pair \( (a, b) \) is not the same as \( (b, a) \) when \( a \neq b \). Order matters in ordered pairs.
- Reason R: (4, -3) lies in quadrant IV.
- In the Cartesian coordinate system, the fourth quadrant (Quadrant IV) contains points where the x-coordinate is positive and the y-coordinate is negative. Since (4, -3) has a positive x-value and a negative y-value, this statement is also true.
Now, does Reason R explain Assertion A?
- No, because the fact that (4, -3) is in Quadrant IV has nothing to do with why \( (a, b) \neq (b, a) \) when \( a \neq b \).
Thus, the correct answer is:
(B) Both A and R are true but R is not the correct explanation of A.
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