1. INSTRUCTIONS: Choose the letter of the correct answer for each item number. Use this test paper as your answer sheet. 1. Which of the following is a well - defined set? A. The set of big people. B. The set of happy people. C. The set of prime numbers. D. The set of intelligent teachers. 2. What is the cardinality of P = the set of days in a week? A. 5 B. 6 C. 7 D. 8
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The set of prime numbers is the set of positive integers greater than 1 that have no positive divisors other than 1 and itself. Show more…
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Test I. State whether each of the following sets is WELL-DEFINED or NOT. ___________ 1. The set of happy people ___________ 2. The set of enjoyable subjects in high school ___________ 3. The set of good teachers ___________ 4. The set of even counting numbers ___________ 5. The set of prime numbers ___________ 6. The set of all factors of 24 ___________ 7. The set of big people ___________ 8. The set of all even numbers from 2 to 10 ___________ 9. The set of hardworking frontline workers ___________ 10. The set of responsible citizens.
Derek F.
5 Let ρ be the relation on the power set P(S) of a finite set S of cardinality n defined ρ by (A, B) ∈ ρ iff A ∩ B = ∅. a. Consider the specific case n = 3, and determine the cardinality of the set ρ. b. What is the cardinality of ρ for an arbitrary n? Express your answer in terms of n. (Hint: There are three places that each element of S can go in building an element of ρ.)
Adi S.
For any integer n, define F(n) = {p ∈ ℤ | n^4 + 1 = p^4 + 1}. Then let P be the partition of the integers that contains all the sets F(n). That is: P = {F(n) | n ∈ ℤ}. Then the cardinality of P (i.e. the number of elements in P) is
Apratim D.
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