Answer:
Check the explanation
Explanation:
Z -> the set of all integers
Z+ -> the set of all positive integers
Z- -> the set of all negative integers
A -> the set of all integers evenly divisible by 3
B -> {4,5,9,10}
C -> {2,4,11,14}
D -> {3,6,9}
E -> {4,6,16}
Questions:
a. B U C
Answer: {2,4,5,9,10,11,14}
b. A ∩ D
Answer: {3,6,9}
c. A ∩ C
Answer: {} or null set or ∅
d. (B⊕D) ⊕ E
Answer:
A ⊕ B denotes the Symmetric difference between A and B.
The result of the operation is the elements that in either of the sets but not in their intersection.
For the question
B -> {4,5,9,10}
D -> {3,6,9}
Elements that are not in the intersection of the two sets that are.
{3,4,5,6,10} here 9 is omitted because it is present in both the sets.
{3,4,5,6,10} ⊕ E
E -> {4,6,16}
The result will be {3,5,19,16} here 4,6 are the intersection of both sets.
So the answer is {3,5,19,16}
e. A U D
Answer: the set of all integers divisible evenly by 3.
f. E – D
Answer: {4,16}
g. D – E
Answer: {3,9}
h. (Z – Z+) – Z-
Answer: (Z – Z+) means remove all the integers from Z that are present in Z+ which results all the negative integers and 0.
({0,Z-} – Z- ) results in {0}.
So the final answer is {0}
