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:
To determine the value of each set of problems, we need to know what each symbols convey:
This represents union which involves combining elements from set M and set P.
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}
This represents an intersection that involves only values that are in both sets.
N ∩ M = {5, 10}
The apostrophe sign after the letter of the set represents values that aren't in that set.
N' = {8,11,12,13}
We'll combine what we learned above here.
M ∩ N' = {8, 11}
P ∪ (M ∩ N') = {5, 8, 11}
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