If set M consists of all integer numbers x such that 3<x<7, and set N consists of all integer numbers x such that 6≤x≤9, list:
M=...
N=...
M∪N=...
M∩N=...
M∖N=...
N∖M=...
Listing M would be the set of all the elements in M, which would be 4,5,6. Listing N would be the same idea, the answer being 6,7,8,9. The third one is the union of the two sets, so you list out all the elements of M and N, but because the number 6 is listed twice, you only write it once. The answer is 4,5,6,7,8,9. The fourth one is the intersection of the two sets, or what they have I common. The only number that is in both sets in 6, so that's the answer. In the fifth and sixth ones, the diagonal line is not a division sign, but a subtraction sign, as we are dealing with sets. Since the fifth one is M/N, we are subtracting the numbers in set N from the numbers in set M. As, once again, 6 is the only common number, subtracting that from set M would leave you with only two numbers, those being 4 and 5. The sixth one is just like the fifth, except it is N/M, so you would subtract the intersection, or I this case, the number six, from the numbers in set N, which would leave you with only three numbers, those being 7,8, and 9. Hope this helped. :)
I would start by listing the sets:
M = {4, 5, 6}
N = {6, 7, 8, 9}
Now do what it asks for in each part.
I assume you know what your notations mean and do.
Actually I have never see M∖N
M = {4, 5, 6}
N = {6, 7, 8, 9}
M∪N = {4, 5, 6, 7, 8, 9}
M∩N = {6}
M∖N = {4, 5}
N∖M = {7, 8, 9}
Please note that these sets are no laughing matter, but here's a joke for good measure: Why don't scientists trust atoms?
Because they make up everything!
To list the sets M and N, as well as their unions, intersections, and differences, we can follow these steps:
1. Set M consists of all integer numbers x such that 3 < x < 7.
M = {4, 5, 6}
2. Set N consists of all integer numbers x such that 6 ≤ x ≤ 9.
N = {6, 7, 8, 9}
3. To find the union (M ∪ N), we combine all the unique elements from both sets.
M ∪ N = {4, 5, 6, 7, 8, 9}
4. To find the intersection (M ∩ N), we identify the common elements between both sets.
M ∩ N = {6}
5. To find the set difference (M \ N), we remove the elements from M that are also present in N.
M \ N = {4, 5}
6. To find the set difference (N \ M), we remove the elements from N that are also present in M.
N \ M = {7, 8, 9}
So, the final lists are:
M = {4, 5, 6}
N = {6, 7, 8, 9}
M ∪ N = {4, 5, 6, 7, 8, 9}
M ∩ N = {6}
M \ N = {4, 5}
N \ M = {7, 8, 9}
To list the sets M and N, as well as their union (M∪N), intersection (M∩N), difference (M∖N), and reverse difference (N∖M), we need to understand the given conditions and apply the relevant set operations.
1. Set M consists of all integer numbers x such that 3 < x < 7.
Therefore, M = {4, 5, 6} since 4, 5, and 6 are the only integers that satisfy 3 < x < 7.
2. Set N consists of all integer numbers x such that 6 ≤ x ≤ 9.
Therefore, N = {6, 7, 8, 9} since 6, 7, 8, and 9 are the only integers that satisfy 6 ≤ x ≤ 9.
3. The union of sets M and N (M∪N) consists of all elements that are in either set M or set N.
Therefore, M∪N = {4, 5, 6, 7, 8, 9} since it includes all the unique elements from both sets.
4. The intersection of sets M and N (M∩N) consists of all elements that are present in both set M and set N.
Since there are no common elements between M and N, M∩N = {} (the empty set).
5. The difference of set M with respect to set N (M∖N) consists of all elements that are in set M but not in set N.
Therefore, M∖N = {4, 5} since 4 and 5 are the elements in M that are not in N.
6. The difference of set N with respect to set M (N∖M) consists of all elements that are in set N but not in set M.
Therefore, N∖M = {7, 8, 9} since 7, 8, and 9 are the elements in N that are not in M.
To summarize:
M = {4, 5, 6}
N = {6, 7, 8, 9}
M∪N = {4, 5, 6, 7, 8, 9}
M∩N = {}
M∖N = {4, 5}
N∖M = {7, 8, 9}