U={All positive integers less than or equal to 30}
M={All even number less than or equal to 20}
N={All odd number less than or equal to 19}
S={All nteger x:10x30}
N(u)
N(n)
N(n)+n(s)
N(m)+n(s)
N(m)+n(n)
To solve the given set operations, we need to understand the definitions of the sets U, M, N, and S:
U = {All positive integers less than or equal to 30}
M = {All even numbers less than or equal to 20}
N = {All odd numbers less than or equal to 19}
S = {All integers x: 10 ≤ x ≤ 30}
Now let's solve the set operations:
1. N(U): This represents the intersection (common elements) between the set N and U. As N consists of only odd numbers and U consists of all positive integers, N(U) will be the set of odd numbers that are less than or equal to 19. Hence, N(U) = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}.
2. N(N): This represents the intersection between the set N and itself. Since N only contains odd numbers, the intersection of N with itself is simply N itself. Hence, N(N) = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}.
3. N(N) + N(S): This represents the union (combination of elements) between N(N) and N(S). N(N) contains odd numbers less than or equal to 19, and N(S) contains all integers between 10 and 30. The union of these two sets will include all odd numbers less than or equal to 19, as well as the integers between 10 and 30 (since they are also odd). Hence, N(N) + N(S) = {1, 3, 5, 7, 9, 10, 11, 13, 15, 17, 19, 20, 21, 23, 25, 27, 29}.
4. N(M) + N(S): This represents the union between N(M) and N(S). N(M) contains no numbers since M only contains even numbers, and N(S) contains all integers between 10 and 30. Hence, N(M) + N(S) = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29}.
5. N(M) + N(N): This represents the union between N(M) and N(N). N(M) contains no numbers since M only contains even numbers, and N(N) contains odd numbers less than or equal to 19. Hence, N(M) + N(N) = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}.