Determine whether there is a one-to-one correspondence between the two sets. {Mon, Tue, Wed} and
{Oct, Nov, Dec}
Two sets have a one-to-one correspondence between them when they have the same cardinality, i.e. number of distinct members in each set. (note: by definition of a set, all members of a set are distinct).
The cardinality of both sets are 3, so the answer is yes.
To determine whether there is a one-to-one correspondence between the two sets, we need to check if there is a unique mapping between each element in one set to an element in the other set.
In this case, there is a one-to-one correspondence between the two sets if each day of the week (Mon, Tue, Wed) corresponds to a unique month (Oct, Nov, Dec) and vice versa.
Let's check:
1. Mon -> ?
2. Tue -> ?
3. Wed -> ?
1. Mon can correspond to either Oct or Nov or Dec.
2. Tue can correspond to either Oct or Nov or Dec.
3. Wed can correspond to either Oct or Nov or Dec.
Since each day of the week can correspond to any of the three months and vice versa, there is no unique mapping between the two sets. Therefore, there is no one-to-one correspondence between the sets {Mon, Tue, Wed} and {Oct, Nov, Dec}.
To determine whether there is a one-to-one correspondence between two sets, you need to check if each element in one set corresponds to exactly one element in the other set, and vice versa.
In this case, we need to check if each day in the set {Mon, Tue, Wed} has exactly one corresponding month in the set {Oct, Nov, Dec}, and vice versa.
To do this, we can visually compare the two sets by aligning each day with its corresponding month:
Mon corresponds to Oct
Tue corresponds to Nov
Wed corresponds to Dec
Since every day in the first set has exactly one corresponding month in the second set, and every month in the second set has exactly one corresponding day in the first set, we can conclude that there is a one-to-one correspondence between the two sets.