contestada

Given the following sets:
U = {2, 7, 10, 15, 22, 27, 31, 37, 45, 55}
A = {10, 22, 27, 37, 45, 55}
B = {2, 15, 31, 37}
C = {7, 10, 15, 37}
Give the set Ac U (B ∩ C).
a) {2, 7, 10, 31, 37}
b) {2, 7, 15, 31, 37}
c) {2, 10, 15, 31, 37}
d) {2, 7, 15, 27, 37}
e) ∅
f) None of the above.

Respuesta :

Answer:

b) {2, 7, 15, 31, 37}

Step-by-step explanation:

Ac is the complement of A, that is, the elements that are in the U(universe) but not in A.

Ac - {2,7,15,31}

[tex]B \cap C[/tex] are the elements that are in both B and C. So

(B ∩ C) = {15,37}

Ac U (B ∩ C) are the elements that are in at least one of Ac or (B ∩ C).

Ac U (B ∩ C) = {2,7,15,31,37}

So the correct answer is:

b) {2, 7, 15, 31, 37}

Answer:

Option b) is correct ie., [tex]A^{c}\bigcup (B \bigcap C)={\{2, 7, 15, 31, 37\}}[/tex]

Step-by-step explanation:

Given sets are

[tex]U ={\{2, 7, 10, 15, 22, 27, 31, 37, 45, 55\}}[/tex]

[tex]A = {\{10, 22, 27, 37, 45, 55\}}[/tex]

[tex]B = {\{2, 15, 31, 37\}}[/tex]

[tex]C = {\{7, 10, 15, 37\}}[/tex]

To find  [tex]A^{c}\bigcup (B \bigcap C)[/tex]

First to find [tex]A^{c}[/tex]

[tex]A^{c}={\{2,7,15,31\}}[/tex]

to find  [tex]B\cap C[/tex]

[tex]B\cap C={\{2, 15, 31, 37\}}\cap {\{7, 10, 15, 37\}}[/tex]

[tex]B\cap C={\{37,15\}}[/tex]

[tex]A^{c}\bigcup (B \bigcap C)={\{2,7,15,31\}}\cup {\{37,15\}}[/tex]

[tex]A^{c}\bigcup (B \bigcap C)={\{2,7,15,31,37\}}[/tex]

Therefore option b) is correct

Therefore  [tex]A^{c}\bigcup (B \bigcap C)={\{2,7,15,31,37\}}[/tex]