Question

Let A and B be sets. Prove that (A∪B)\(A∩B) = (A\B)∪(B\A)

Answer #1

Let A and B be sets. Prove that A ⊆ B if and only if A − B =
∅.

Let A, B, C
be sets. Prove that
(A \ B) \ C = (A \ C) \ (B
\ C).

Problem 3.9. Let A and B be sets. Prove that A × ∅ = ∅ × B =
∅.
Please write your answer as clearly as possible, appreciate
it!

Let A, B, C and D be sets. Prove that A \ B and C \ D are
disjoint if and only if A ∩ C ⊆ B ∪ D.

Let A, B, C and D be sets. Prove that A\B ⊆ C \D if and only if
A ⊆ B ∪C and A∩D ⊆ B

Let A and B be nonempty sets. Prove that if f is an injection,
then f(A − B) = f(A) − f(B)

Let A and B be nonempty sets. Prove that if f is an injection,
then f(A − B) = f(A) − f(B)

Let A,B and C be sets, show(Prove) that (A-B)-C =
(A-C)-(B-C).

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.

Let A and B be sets. Consider the following statement: A ∪ (B −
A) ⊆ A ∪ B
a) Draw and label a Venn diagram to illustrate this
statement.
b) Prove this statement.
please clearly show illustration and work

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 29 minutes ago

asked 35 minutes ago

asked 40 minutes ago

asked 43 minutes ago

asked 50 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago