Consider the following definition. Definition 1. Let S denote a set. We say that S is primal if 0 ∈S or 1 ∈S (i) Which of the following sets are primal? [Explain your answer.] a. {x ∈Z: −3 < x and x < 6} b. {n ∈Z: n ≡10 mod 3} c. ∅ d. {n2−15: n ∈Z} (ii) Prove or disprove: The intersection of two primal sets is primal. (iii) Prove or disprove: If S is primal and T ⊇S, then T is primal. (iv) Prove or disprove: If S is not primal,
Consider the following definition. Definition 1. Let S denote a set. We say that S is primal if 0 ∈S or 1 ∈S (i) Which of the following sets are primal? [Explain your answer.] a. {x ∈Z: −3 < x and x < 6} b. {n ∈Z: n ≡10 mod 3} c. ∅ d. {n2−15: n ∈Z} (ii) Prove or disprove: The intersection of two primal sets is primal. (iii) Prove or disprove: If S is primal and T ⊇S, then T is primal. (iv) Prove or disprove: If S is not primal,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following definition.
Definition 1. Let S denote a set. We say that S is primal if 0 ∈S or 1 ∈S
(i) Which of the following sets are primal? [Explain your answer.]
a. {x ∈Z: −3 < x and x < 6}
b. {n ∈Z: n ≡10 mod 3}
c. ∅
d. {n2−15: n ∈Z}
(ii) Prove or disprove: The intersection of two primal sets is primal.
(iii) Prove or disprove: If S is primal and T ⊇S, then T is primal.
(iv) Prove or disprove: If S is not primal, then Z\S is primal.
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