If two sets A and B have p and q no. of elements respectively and f: A →B is one-one, then the r

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If two sets A and B have p and q no. of elements...

If two sets $\mathrm{A}$ and $\mathrm{B}$ have $\mathrm{p}$ and $\mathrm{q}$ no. of elements respectively and $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ is one-one, then the relation between $\mathrm{p}$ and $\mathrm{q}$ is (1) $\mathrm{p} \geq \mathrm{q}$ (2) $\mathrm{p}>\mathrm{q}$ (3) $\mathrm{p} \leq \mathrm{q}$ (4) $\mathrm{p}=\mathrm{q}$

If two sets $\mathrm{A}$ and $\mathrm{B}$ have $\mathrm{p}$ and $\mathrm{q}$ no. of elements respectively and $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ is one-one, then the relation between $\mathrm{p}$ and $\mathrm{q}$ is
(1) $\mathrm{p} \geq \mathrm{q}$
(2) $\mathrm{p}>\mathrm{q}$
(3) $\mathrm{p} \leq \mathrm{q}$
(4) $\mathrm{p}=\mathrm{q}$

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Key Concepts

Injective Function

An injective function (or one-to-one function) is a mapping where each element of the domain is associated with a distinct element in the codomain, ensuring no two different elements from the domain share the same image in the codomain.

Cardinality

Cardinality refers to the measure of the number of elements in a set. When a one-to-one function exists from one set to another, it implies that the number of elements in the domain is less than or equal to the number of elements in the codomain.

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