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Study the Assertion and Reason and choose the correct option.
If Set A has m elements, Set B has n elements and n < m, then the number of one-one function(s)…
Assertion: If Set $A$ has $m$ elements, Set $B$ has $n$ elements and $n < m$, then the number of one-one function(s) from $A \to B$ is zero.
Reason: A function $f: A \to B$ is defined only if all elements in Set $A$ have an image in Set $B$.
- (a)Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
- (b)Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
- (c)Assertion is true and Reason is false.
- (d)Assertion is false and Reason is true.
Answer
Answer
Correct option: (b)
Answer: (b) Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
With $n<m$ two elements of $A$ must share an image, so no one-one function exists. The Reason is the definition of a function and does not explain this.