(9) Suppose that we are given f : A → B and subsets X ⊂ A respectively Y ⊂ B so that we can define the direct image f(X) ⊂ B and the inverse image f^−1(Y ) ⊂ A. So that if X ⊂ A, then f(X) is a set and if Y ⊂ B, then f^−1(Y) is a set; you are proving things about these definitions. (a) Prove that f^−1(X ∪ Y ) = f^−1(X) ∪ f^−1(Y ). (b) Prove that if f is surjective then Y ⊂ f(f^−1(Y )).
(9) Suppose that we are given f : A → B and subsets X ⊂ A respectively Y ⊂ B so that we can define the direct image f(X) ⊂ B and the inverse image f^−1(Y ) ⊂ A. So that if X ⊂ A, then f(X) is a set and if Y ⊂ B, then f^−1(Y) is a set; you are proving things about these definitions. (a) Prove that f^−1(X ∪ Y ) = f^−1(X) ∪ f^−1(Y ). (b) Prove that if f is surjective then Y ⊂ f(f^−1(Y )).
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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(9) Suppose that we are given f : A → B and subsets X ⊂ A respectively Y ⊂ B so that we can define the direct image f(X) ⊂ B and the inverse image f^−1(Y ) ⊂ A.
So that if X ⊂ A, then f(X) is a set and if Y ⊂ B, then f^−1(Y) is a set; you are proving things about these definitions.
(a) Prove that f^−1(X ∪ Y ) = f^−1(X) ∪ f^−1(Y ).
(b) Prove that if f is surjective then Y ⊂ f(f^−1(Y )).
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