Explore BrainMass
Share

Prove the the function of the union of two sets

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

Theorem 4.16

Let f: A --> B, C and D be subsets of A, and E and F be subsets of B. Then

b) f(the union of C and D) = the union of f(C) and f(D)
d) f^-1(the union of E and F) = the union of f^-1(E) and f^-1(F).

See the attached file.

© BrainMass Inc. brainmass.com October 24, 2018, 11:03 pm ad1c9bdddf
https://brainmass.com/math/computing-values-of-functions/prove-function-union-sets-179725

Attachments

Solution Summary

This is a proof regarding functions, intersections, and subsets provided in an attached Word document.

$2.19
See Also This Related BrainMass Solution

Proof about Functions

Let f: X-->Y be a function from one set X to another set Y, let S be a subset of X, and let U be a subset of Y. What in general can one say about f^-1(f(S)) and S? What about f(f^-1(U)) and U?

View Full Posting Details