Question

Let A, B be sets and f: A -> B. For any subsets X,Y subset of...

Let A, B be sets and f: A -> B. For any subsets X,Y subset of A, X is a subset of Y iff f(x) is a subset of f(Y).

Prove your answer. If the statement is false indicate an additional hypothesis the would make the statement true.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let F be an ordered field.  Let S be the subset [a,b) i.e, {x|a<=x<b, x element of...
Let F be an ordered field.  Let S be the subset [a,b) i.e, {x|a<=x<b, x element of F}. Prove that infimum and supremum exist or do not exist.
Let f : X → Y and suppose that {Ai}i∈I is an indexed collection of subsets...
Let f : X → Y and suppose that {Ai}i∈I is an indexed collection of subsets of X. Show that f[∩i∈IAi ] ⊆ ∩i∈I f[Ai ]. Give an example, using two sets A1 and A2, to show that it’s possible for the LHS to be empty while the RHS is non-empty.
Let X, Y and Z be sets. Let f : X → Y and g :...
Let X, Y and Z be sets. Let f : X → Y and g : Y → Z functions. (a) (3 Pts.) Show that if g ◦ f is an injective function, then f is an injective function. (b) (2 Pts.) Find examples of sets X, Y and Z and functions f : X → Y and g : Y → Z such that g ◦ f is injective but g is not injective. (c) (3 Pts.) Show that...
Let f : A → B be a function and let A1 and A2 be subsets...
Let f : A → B be a function and let A1 and A2 be subsets of A. Prove that if f is one-to-one, then f(A1 ∩ A2) = f(A1) ∩ f(A2).
Is the following statement true? "If f (Y − X) = f (Y ) − f...
Is the following statement true? "If f (Y − X) = f (Y ) − f (X) for all sets X and Y with X ⊆ Y ⊆ A, then f : A → B is injective." Please provide a proof if it is true, and a counterexample if it is false.
Let f : A → B and g : B → C. For each of the...
Let f : A → B and g : B → C. For each of the statements in this problem determine if the statement is true or false. No explanation is required. Just put a T or F to the left of each statement. a. g ◦ f : A → C b. If g ◦ f is onto C, then g is onto C. c. If g ◦ f is 1-1, then g is 1-1. d. Every subset of...
Using any method, show that for all sets A and B which are subsets of a...
Using any method, show that for all sets A and B which are subsets of a universe U, that A − (A − B) = A ∩ B. Note. No proofs by Venn diagram will be accepted.** Algebraic Prove should be good.
Let A, B, C be sets and let f : A → B and g :...
Let A, B, C be sets and let f : A → B and g : f (A) → C be one-to-one functions. Prove that their composition g ◦ f , defined by g ◦ f (x) = g(f (x)), is also one-to-one.
For a given set X, consider the family F of its subsets Y such that at...
For a given set X, consider the family F of its subsets Y such that at least one of Y or X\Y is finite. Prove that F is a set algebra. When is F a sigma-algebra? Prove it.
10. Prove if X and Y are nonempty closed subsets of [a,b]⊂ ℝ such that X∪Y=[a,b],...
10. Prove if X and Y are nonempty closed subsets of [a,b]⊂ ℝ such that X∪Y=[a,b], then X∩Y≠ ∅.