Practice questions on Sets and Binary Relation properties r,s,t,a,i
Also tribute to 10001 magazine and/or to left back field hockey defense, which both relate to Biction

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  1. Suppose we are using the letters from the word MASSACHUSETTS. How many distinct words (permutations) are there for the letters in the word MASSACHUSETTS?

  2. Suppose we are using the letters from the word PANTHERS. How many distinct words (permutations) are there for the letters in the word PANTHERS?

  3. Suppose we are using the letters from the word DISCRETE. How many distinct words (permutations) are there for the letters in the word DISCRETE?

  4. What is the cardinality of the PowerSet of the set consisting of the letters in the word PANTHERS?
    | PowerSet{P, A, N, T, H, E, R, S} | = ?

  5. Let PowerSetPan = PowerSet of the set of letters in the word PANTHERS.
    Let P3 = {x | x isAnElementOf PowerSetPan and cardinality(x) = 3}.
    Stated another way, set P3 = { x | x isMemberOf PowerSetPan and | x | = 3 }
    .
    What is cardinality(P3)? | P3 | = ?

  6. Let A = {1, 2, 3, 4, 5} and let S1 = {(x,y) | x = y or x squared = y}.
    What is the cardinality of set S1?
    1 2 3 4 5 6 7 8 9 10 11 12 13 14

  7. Let A = {1, 2, 3, 4, 5} and let S2 = {(x,y) | x < y}.
    What is the cardinality of set S2?
    1 2 3 4 5 6 7 8 9 10 11 12 13 14

  8. Let A = {1, 2, 3, 4, 5} and let S3 = {(x,y) | x mod 2 = y mod 2}.
    What is the cardinality of set S3?
    1 2 3 4 5 6 7 8 9 10 11 12 13 14

  9. Let S4 = S1 intersection S3.
    What is the cardinality of set S4?
    1 2 3 4 5 6 7 8 9 10 11 12 13 14

  10. Let S5 = S1 intersection S2.
    What is the cardinality of set S5?
    1 2 3 4 5 6 7 8 9 10 11 12 13 14

  11. Let S6 = S2 intersection S3.
    What is the cardinality of set S6?
    1 2 3 4 5 6 7 8 9 10 11 12 13 14

  12. What properties does the Binary Relation S1 have?
      reflexive symmetric transitive antisymmetric irreflexive

  13. What properties does the Binary Relation S2 have?
      reflexive symmetric transitive antisymmetric irreflexive

  14. What properties does the Binary Relation S3 have?
      reflexive
      symmetric
      transitive
      antisymmetric
      irreflexive
  15. What properties does the Binary Relation S6 have?
      reflexive
      symmetric
      transitive
      antisymmetric
      irreflexive
  16. Which of the following binary numbers is equal to decimal value 3,125?
    110000010101 110000110101 110010011100

  17. Which of the following binary numbers is equal to decimal value 3,229?
    110111010101 110110110101 110010011101