Is R closed over addition? (Y/N) Is N closed over addition? (Y/N) Is Z closed over subtraction? (Y/N)

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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Question
  1. Is R closed over addition? (Y/N)

  2. Is N closed over addition? (Y/N)

  3. Is Z closed over subtraction? (Y/N)

  4. Is N closed over subtraction? (Y/N)

  5. Is Q closed over multiplication? (Y/N)

  6. Is N closed over multiplication? (Y/N)

  7. Is Z closed over division? (Y/N)

  8. Is R closed over division? (Y/N)

  9. Is the cardinality of a set the sum of all of the numbers inside the set? (Y/N)

  10. Is the union of two sets the common terms between the two sets? (Y/N)

  11. Is the intersection of two sets when we can find all the items in one set, in the other set? (Y/N)

  12. If there is such a thing as an empty set, which contains nothing, can there be a “full set” that contains everything? (Y/N)

  13. In a bivalent logical system, can a proposition have more than two truth values? (Y/N)

  14. In a bivalent logical system, if I demonstrate that assuming a given proposition is true causes a contradiction, can I conclude that the proposition is false? (Y/N)

  15. Does a truth table evaluate all possible scenarios for a given proposition? (Y/N)

  16. Is the relation of “mapping” between two sets used to determine cardinality - and not used to determine the subset relation? (Y/N)

  17. Is it true that the null set is a subset of every other set? (Y/N)

  18. If A is a subset of B, and B is a subset of A, then does A =B? (Y/N)

  19. If A maps onto B, and if B maps onto A, then does |A|=|B|? (Y/N)

  20. If the A is a subset of B, does A∪B=A? (Y/N)

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