Question
Download Solution PDFIf A = { x : x is a multiple of 3} and B = (x : x is a multiple of 4} and C = {x : x is a multiple of 12}, then which one of the following is a null set?
where A \ B: Set A with the elements that are not in set B removed. This is also known as the set difference between A and B.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- Null set is the set that does not contain anything.
- In mathematical sets, the null set, also called the empty set,
- It is symbolized or { }.
Calculation:
Given:
A = {x : x is a multiple of 3}
∴ A = {3, 6, 9, 12, 15, 18, 24…}
B = {x : x is a multiple of 4}
∴ B = {4, 8, 12, 16, 20, 24, 28, 32 ...}
C = {x : x is a multiple of 12}
∴ C = {12, 24, 36, 48, 60, 72, 84, 96 ...}
Now,
A∩B = {12, 24 ...} = C
∴ (A∩B) \ C = { } = Null set
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