Let A, B, and C be as in, let D = {3, 2}, and let E = {2, 3, 2}. Determine which of the following are true. Give reasons for your decisions.

a. A = B

b. B = C

c. B = D

d. E = D

e. A ∩ B = B ∩ A

f. A ∪ B = B ∪ A

g. A - B = B - A

h. A ⊕ B = B ⊕ A

The question is incomplete. Below is the complete question "Let A = {0,2,3}, B = {2,3}, C = {1,5,9}, D={3,2}, and let E={2,3,2}. Determine which of the following are true. Give reasons for your decisions.

a. A = B

b. B = C

c. B = D

d. E = D

e. A ∩ B = B ∩ A

f. A ∪ B = B ∪ A

g. A - B = B - A

h. A ⊕ B = B ⊕ A"

Answer

a. A = B (false)

b. B = C (false)

c. B = D (true)

d. E = D (true)

e. A ∩ B = B ∩ A (true)

f. A ∪ B = B ∪ A (true)

g. A - B = B - A (true)

h. A ⊕ B = B ⊕ A" (true)

Step-by-step explanation:

A. the notation A=B simply means if set A equals set B from the above we can conclude that set A has 3 elements while set B has only two elements, hence the statement is false.

B. The notation B=C simply means if set B equals set C from the above we can conclude that the sets are not equal since both sets has a different elements

C. The notation B=D simply means if set B equals set D from the above we can conclude that the sets are equal since both sets has the same elements irrespective of the arrangement.

D. The notation D=E simply means if set B equals set D from the above we can conclude that the sets are equal since both sets has the same elements irrespective of the repetition

e. the set

AnB={0,2,3}n{2,3}

AnB={2,3}

also

BnA={2,3}n{0,2,3}

BnA={2,3}

hence A ∩ B = B ∩ A is true

f. A ∪ B={0,2,3}u{2,3}

A ∪ B={0,2,3}

also

B ∪ A={2,3}u{0,2,3}

B ∪ A={0,2,3}

Hence A ∪ B = B ∪ A

g. The difference between two sets is the set of values in one but not the other

Hence

A-B={0,2,3}-{2,3}

A-B={0}

also B - A={2,3}-{0,2,3}

B - A={0}

Hence A - B = B - A is true

h. A ⊕ B is the Symmetric difference is those elements that belong to one set, but not the other, it is express as

A ⊕ B = (A U B) - (A ∩ B)

also B ⊕ A = (BU A) - (B ∩ A)

comparing both

A ⊕ B=B ⊕ A

(A U B) - (A ∩ B) = (BU A) - (B ∩ A)

{0,2,3}-{2,3}={0,2,3}-{2,3}

{0}={0}

we can therefore conclude that A ⊕ B = B ⊕ A is true