course Mth 151
7/9 12
Open QA4:`q001. From the collection of letters a, b, c, d, e, how many smaller collections having at least one element may be formed?
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Your solution:
2^n-2 because you are dealing with small subsets so it would be 2^5-2=30 so there are 30 small subsets
3
Ok
`q002. A one-to-one correspondence between two sets is a rule that associates each element of the each with exactly one element of the other. A natural one-to-one correspondence between the sets { a, b, c } and { 1, 2, 3 } would be to associate a with 1, b with 2, c with 3. This correspondence might be represented as [ a <--> 1, b <--> 2, c <--> 3 ].
This isn't the only possible one-to-one correspondence between these sets. Another might be [ a <--> 2, b <--> 1, c <--> 3 ]. In each case, every element of each set is associated with exactly one element of the other.
Another correspondence between the sets might be [ a <--> 3, b<-->2, c<-->3 ]. This correspondence is not one-to-one. In what way does it fail to be a one-to-one correspondence (remember that a one-to-one correspondence is one in which every element of each set is associated with exactly one element of the other).
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Your solution:
It is not one to one because the 3 is with element a and c so each element is not represented
3
Ok
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Question: `q003. There are four possible one-to-one correspondences between the sets {a, b, c} and {1, 2, 3} which were not described in the preceding exercise. One of them would be [ a <--> 3, b <--> 2, c <--> 1 ]. What are the other three possible one-to-one correspondences?
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Your solution:
[a < - - > 2, b < - - > 1, c < - - > 3], [a < - - > 1, b < - - > 3, c < - - > 2], [ a < - - > 1, b < - - > 2, c < - - > 3]
3
Ok
`q004. Explain why it is not possible to put the sets { a, b, c} and {1, 2, 3, 4} into a one-to-one correspondence.
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Your solution:
Because you do not have equal amounts of elements
3
Ok
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