Let $A$ and $B$ be two different sets with the same cardinality. Then what can we say (true or false) about the statement: " corresponding to every subset $X$ of $A$ , there exist a subset $Y$ of $B$ such that $X$ and $Y$ have the same cardinality." ?
2026-04-06 11:34:24.1775475264
A question on equipotency of sets
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Hint: If $f\colon A\to B$ is a bijection, then whenever $X\subseteq A$, the restriction of $f$ to $X$ is a bijection with $f[X]$.