Let A be the set of all 50 cards numbered from 1 to 50. Let f: A → mathbbN be a function defined by f(x) = card number of the card ‘x’. Then the function…

Answer: (a) one to one but not onto. Distinct cards have distinct numbers, so f is one to one. Its range is {1, 2, …, 50}, which is a proper subset of mathbbN, so f is not onto. Correct: (a)

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Mathematics20231 markMCQRelations and Functions

Choose the correct option.

Let A be the set of all 50 cards numbered from 1 to 50. Let f: A → mathbbN be a function defined by…

Let $A$ be the set of all $50$ cards numbered from $1$ to $50$. Let $f: A \to \mathbb{N}$ be a function defined by $f(x) =$ card number of the card ‘$x$’. Then the function ‘$f$’ is:

(a)one to one but not onto.
(b)onto but not one to one.
(c)neither one to one nor onto.
(d)one to one and onto.

Answer

Correct option: (a)

Answer: (a) one to one but not onto. Distinct cards have distinct numbers, so $f$ is one to one. Its range is $\{1, 2, \dots, 50\}$, which is a proper subset of $\mathbb{N}$, so $f$ is not onto.