The answer:
a. A ∩ C = {1, 3, 5, 7, 9}
b. B ∩ C = { - }
c. A ∩ B = {2, 4, 6, 8, 10}
d. A U B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
e. B U C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Step by Step explanation:
Universal set is a collection of certain objects that have a clear definition and are considered as a single entity.
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B = {2, 4, 6, 8, 10}
C = {1, 3, 5, 7, 9}
a. A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
The intersection contains all the elements in both sets, so:
A ∩ C = {1, 3, 5, 7, 9}
b. B = {2, 4, 6, 8, 10}
The intersection contains all the elements in both sets, in this
question, nothing is the same, so:
B ∩ C = { - }
c. A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A ∩ B = {2, 4, 6, 8, 10}
d. A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
The union contains all the elements in either set, so:
A U B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, Notice we only list 2, 4, 6, 8, 10
once.
e. B = {2, 4, 6, 8, 10}
B U C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
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Answers & Comments
Verified answer
The answer:
a. A ∩ C = {1, 3, 5, 7, 9}
b. B ∩ C = { - }
c. A ∩ B = {2, 4, 6, 8, 10}
d. A U B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
e. B U C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Step by Step explanation:
Universal set is a collection of certain objects that have a clear definition and are considered as a single entity.
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B = {2, 4, 6, 8, 10}
C = {1, 3, 5, 7, 9}
a. A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
C = {1, 3, 5, 7, 9}
The intersection contains all the elements in both sets, so:
A ∩ C = {1, 3, 5, 7, 9}
b. B = {2, 4, 6, 8, 10}
C = {1, 3, 5, 7, 9}
The intersection contains all the elements in both sets, in this
question, nothing is the same, so:
B ∩ C = { - }
c. A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B = {2, 4, 6, 8, 10}
The intersection contains all the elements in both sets, so:
A ∩ B = {2, 4, 6, 8, 10}
d. A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B = {2, 4, 6, 8, 10}
The union contains all the elements in either set, so:
A U B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, Notice we only list 2, 4, 6, 8, 10
once.
e. B = {2, 4, 6, 8, 10}
C = {1, 3, 5, 7, 9}
The union contains all the elements in either set, so:
B U C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
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