Answer :
The sets B∪C and B∩C are given as -
B∪C = [2, ∞)
B∩C = [8, ∞]
We have the following sets B and C of real numbers defined as follows -
B = (z| z > 1)
C = (z| z ≥ 8)
We have to determine the sets - B∪C and B∩C using interval notation.
What is a Set in Mathematics? What is the meaning of signs ∪ and ∩ ?
A set is a collection of elements or numbers or objects, represented within the curly brackets { }. For example: {1,2,3,4} is a set of numbers. The sign ∪ denotes the union of two sets whereas ∩ denotes the intersection of two sets.
According to question, we have -
B = (z| z>1)
C = (z| z≥8)
These sets can be written as follows -
B = (z| z>1) = {2, 3, 4, 5 .....}
C = (z| z≥8) = { 8, 9, 10, 11, 12 .....}
Calculating B∪C
B = (z| z>1) = {2, 3, 4, 5 .....}
C = (z| z≥8) = { 8, 9, 10, 11, 12 .....}
B∪C = { 2, 3, 4, 5, 6, 7 .......) = [2, ∞)
Calculating B∩C
B = (z| z>1) = {2, 3, 4, 5 .....}
C = (z| z≥8) = { 8, 9, 10, 11, 12 .....}
B∩C = [8, ∞]
Hence, the sets B∪C and B∩C are given as -
B∪C = [2, ∞)
B∩C = [8, ∞]
To solve more questions on Union and Intersection of sets, visit the link below -
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