Image and Preimage

• Image and Preimage #Card
  • For $A \subset X$ and $B \subset Y$: - Image of $A$ under $R$: $R(A) \text{ or } RA := {y \in Y : \exists x \in A, (x, y) \in R}$ - Preimage of $B$ under $R$: $R^-B := {x \in X : \exists y \in B, (x, y) \in R}$ - Notation: $Rx := R({x})$ and $R^-y := R^-({y})$.

Back

For $A \subset X$ and $B \subset Y$:

• Image of $A$ under $R$: $R(A) \text{ or } RA := {y \in Y : \exists x \in A, (x, y) \in R}$
• Preimage of $B$ under $R$: $R^-B := {x \in X : \exists y \in B, (x, y) \in R}$
• Notation: $Rx := R({x})$ and $R^-y := R^-({y})$.

Lean

Set.image (f '' s), Set.preimage (f ⁻¹' t) / 本ノート relImage, relPreimage