Answer:
Let's work through each of these set operations and represent them graphically. The notations used are as follows:
Parentheses () represent set operations.
A∪B represents the union of sets A and B.
A∩B represents the intersection of sets A and B.
A\B represents the set difference of A and B.
(A∪B)∩C:
(A∪B) is the union of sets A and B, which includes all numbers that are in either A or B.
Then, we take the intersection of the result with set C.
Graphically, it's the overlapping region of the union of A and B with C.
(A∩B)\C:
(A∩B) is the intersection of sets A and B, which includes numbers that are in both A and B.
Then, we take the set difference with C, meaning we remove any elements that are also in C.
Graphically, it's the region of overlap between A and B, excluding any elements in C.
(A∪B)\C:
(A∪B) is the union of sets A and B, which includes all numbers that are in either A or B.
Then, we take the set difference with C, meaning we remove any elements that are also in C.
Graphically, it's the region that includes all elements in either A or B but excludes any elements in C.
(A\B)∩C:
(A\B) is the set difference of A and B, which includes all elements in A that are not in B.
Then, we take the intersection of the result with C.
Graphically, it's the region in A that is not in B and is also in C.
(A\C)∪(B\C):
(A\C) is the set difference of A and C, which includes all elements in A that are not in C.
(B\C) is the set difference of B and C, which includes all elements in B that are not in C.
Then, we take the union of the results.
Graphically, it's the region in A that is not in C combined with the region in B that is not in C.
(A\C)∩(B\C):
(A\C) is the set difference of A and C, which includes all elements in A that are not in C.
(B\C) is the set difference of B and C, which includes all elements in B that are not in C.
Then, we take the intersection of the results.
Graphically, it's the region in A that is not in C and is also in B, excluding any elements in C.
Explanation: