Answer:
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
