course Mth 151 |ğnR~짥䷛assignment #003
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17:22:13 `qNote that there are 4 questions in this assignment. `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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RESPONSE --> There could be 32 smaller collections formed because there are 5 letters, 2^5 is 32. confidence assessment: 3
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17:26:09 `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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RESPONSE --> The group [ a<->3, b<->2, c<->3] contains the number 3 twice. One to one cannot contain a duplicate number or letter. confidence assessment: 3
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17:38:40 `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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RESPONSE --> The other three one-to-one correspondences would be [a<->2, b<->1, c<->3], [a<->3, b<->1, c<->2] and [a<->2, b<->3, c<->1]. confidence assessment: 3
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17:39:55 `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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RESPONSE --> The sets do not have the same elements. One of the numbers in the second set would always be left out. confidence assessment: 3
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