Class 12 Relations And Functions · Assertion Reason1 Markstypes_of_functions

Class 12 Maths · Relations And Functions · Assertion Reason #63

Assertion: An onto function \(f:\{1,2,3\}\to\{1,2,3\}\) is always one-one. Reason: For a function from a three-element set to a three-element set, if two distinct inputs share an image, there can be at most two distinct images, so the function cannot be onto.

(A) Both Assertion and Reason are correct, and the Reason is the correct explanation of the Assertion.
(B) Both Assertion and Reason are correct, but the Reason is not the correct explanation of the Assertion.
(C) The Assertion is correct, but the Reason is incorrect.
(D) The Assertion is incorrect, but the Reason is correct.

✅ Step-by-Step Solution

Final Answer: Option (A): Both Assertion and Reason are correct, and the Reason is the correct explanation of the Assertion.

Both statements are true. A collision between two of the three inputs would leave at most two distinct outputs, so one codomain element would have no preimage. Thus an onto map must have no collision and is one-one. The Reason directly explains the Assertion, giving option a.

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Class 12 Maths · Relations And Functions · Assertion Reason #63

✅ Step-by-Step Solution

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