Suppose that f : X Y is a function, and that A X and B X. a) Prove that f(A B) f(A) f(B). b) Prove that f(A B) = f(A) f(B) given that f is an...
View the step-by-step solution to:

Question

Suppose that f : X → Y is a function, and that A ⊂ X and B ⊂ X.

a) Prove that f(A ∩ B) ⊂ f(A) ∩

f(B).

b) Prove that f(A ∩ B) = f(A) ∩ f(B) given that f is an injective map.

Recently Asked Questions

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

-

Educational Resources
  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question
Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes