Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Given U = {5,6,7,8,9,10,11,12,13}, M = {5,8,10,11}, N = {5,6,7,9,10}, and P = {5,11}. Find each set:
(a) M∪P
(b) N∩M
(c) N'
(d) P∪(M∩N')
(e) Find the number of proper subsets of x.

Sagot :

chibabykalu16

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

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.