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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 :

Chibabykalu16idn

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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