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Questions and Answers
Which of the following sets is the empty set?
Which of the following sets is the empty set?
- { Φ } (correct)
- { O }
- { x: x is an integer and x² - 4x + 3 = 0 }
- { x: x is an integer and 2 < x < 3 } (correct)
How many proper subsets can be formed from the set A = { 1, 2, 3, 4, 5 }?
How many proper subsets can be formed from the set A = { 1, 2, 3, 4, 5 }?
- 63 (correct)
- 31 (correct)
- 32
- 64
What is the solution set for the equation x² - 4x + 3 = 0?
What is the solution set for the equation x² - 4x + 3 = 0?
- { 1, 3 } (correct)
- { 2 }
- { 0, 4 }
- { -1, 1 }
What is the cardinality of set { x: x is an integer and 2 < x < 3 }?
What is the cardinality of set { x: x is an integer and 2 < x < 3 }?
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Study Notes
Empty Set Identification
- The empty set is represented by the symbol Φ.
- Among the given options, {Φ} is considered a set containing an empty set; it is not empty itself.
- Option D, { x: x is an integer and 2 < x < 3 }, does not contain any integers, hence it is the empty set.
Proper Subsets of Set A
- A proper subset is a subset that does not include all the elements of the original set.
- For a set A with n elements, the total number of subsets is 2^n.
- Given A = {1, 2, 3, 4, 5}, it has 5 elements.
- Total subsets of A = 2^5 = 32.
- To find the number of proper subsets, subtract one (the full set itself) from the total: 32 - 1 = 31.
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