Multiple Choice (my answers in parenthesis) 1) Over the set of integers, let R b
ID: 2984994 • Letter: M
Question
Multiple Choice (my answers in parenthesis)
1) Over the set of integers, let R be the relation defined by xRy means: x − y is divisible by 7. The number of sets in this equivalence relation is:
a. infinite
b. 8
c. This is not an equivalence relation
d. 7
e. None of the above.
(?)
2) Let the universe for these statements be the positive integers. The statements: D2(x) = “x is divisible by 2†and D6(x) = “x is divisible by 6.†A formal statement that states divisibility by 6 guarantees divisibility by 2 is:
(A or B)
3)
(B or C)
4) The negation of the statement “I missed the train but my watch was not slow†is:
a. I did not miss the train and my watch was not slow.
b. I missed the train or my watch was slow.
c. I did not miss the train or my watch was slow.
d. I missed the train or my watch was not slow.
e. None of the above.
(B or C)
Other Problems
1) Let the universe be all animals. Write in the language of the predicate logic with proper quantifiers and parentheses the statement: “Some dogs chase any cat.†Let C(x) be “x is a cat, D(x), “ x is a dogâ€, and Ch(r,s), “r chases sâ€.
2)
3) The following binary relation is defined on the set A = {0, 1, 2, 4, 6}: R = {(0, 1), (1, 0), (2, 4), (4, 2), (4, 6), (6, 4), (1, 6)}. Draw the directed graph.
4) A club with 10 women and 7 men needs to form a committee of size 6. Show your answer in terms of C(n,r). Do not give a numerical answer.
(a) How many committees are possible?
(b) How many committees are possible if a committee must have 4 women and 3 men?
(c) How many committees are possible if a committee must consist of all women?
(d) How many committees are possible if a committee must have not less than three women?
Explanation / Answer
c. This is not an equivalence relation
d
b
c
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