Let f : A → B and let A i ⊂ A and B i ⊂ B for i = 0 and i = 1 . Show that f − 1 preserves inclusions, unions, intersections, and differences of sets: Show that f preserves inclusions and unions only: f ( A 0 − A 1 ) ⊃ f ( A 0 ) − f ( A 1 ) ; show that equality holds if f is injective.
Let f : A → B and let A i ⊂ A and B i ⊂ B for i = 0 and i = 1 . Show that f − 1 preserves inclusions, unions, intersections, and differences of sets: Show that f preserves inclusions and unions only: f ( A 0 − A 1 ) ⊃ f ( A 0 ) − f ( A 1 ) ; show that equality holds if f is injective.
Solution Summary: The author explains that if f:Ato B is a subset of A, then it's the set of all images of points.
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY