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Sagot :
Answer:
M ∪ P = {5,8,10,11}
N ∩ M = {5, 10}
N' = {8,11,12,13}
P ∪ (M ∩ N') = {5, 8, 11}
Proper subsets of x = 511
Step-by-step explanation:
Given:
- U = {5,6,7,8,9,10,11,12,13}
- M = {5,8,10,11}
- N = {5,6,7,9,10}
- P = {5,11}
To determine the value of each set of problems, we need to know what each symbols convey:
∪ - e.g M ∪ P
This represents union which involves combining elements from set M and set P.
- M = {5,8,10,11}
- P = {5,11}
Combining them and using only one in case of repetition of sets like the 5 and 11 results in:
M ∪ P = {5,8,10,11}
∩ - e.g N ∩ M
This represents an intersection that involves only values that are in both sets.
- M = {5,8,10,11}
- N = {5,6,7,9,10}
N ∩ M = {5, 10}
' - e.g N'
The apostrophe sign after the letter of the set represents values that aren't in that set.
- N = {5,6,7,9,10}
- [tex]\mathcr{u} = \{{5,6,7,8,9,10,11,12,13\}[/tex]
N' = {8,11,12,13}
Multiple set notations (∪, ∩ and ')
We'll combine what we learned above here.
- M = {5,8,10,11}
- N' = {8,11,12,13}
- P = {5,11}
M ∩ N' = {8, 11}
P ∪ (M ∩ N') = {5, 8, 11}
Proper subsets
Assuming x is a set with n elements, the number of proper subsets of x is 2^n - 1 (all subsets except the set itself). Let's take U as x since it's the universal set.
The number of elements in U is 9 (since U = {5, 6, 7, 8, 9, 10, 11, 12, 13}).
So, the number of proper subsets of U is:
2^9 - 1
= 512 - 1
= 511
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