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Given D = {x | x is a whole number} E = {x | x is a perfect square < 100} F = {x | x is an even number between 10 and 20} 1. D ∩ E {12, 14, 16, 18} 2. D ∩ F {1, 4, 9, 16, 25, 36, 49, 64, 81} 3. D ∩ (E ∩ F) {all whole numbers} 4. D ∪ (E ∩ F) {1, 4, 9, 16, 25, 36, 49, 64, 81, 12, 14, 18} 5. D ∩ (E ∪ F) {16}

Respuesta :

dalendrk
[tex]D=\{0;\ 1;\ 2;\ 3;\ 4;...\}\\E=\{1;\ 4;\ 9;\ 16;\ 25;\ 36;\ 49;\ 64;\ 81\}\\F=\{12;\ 14;\ 16;\ 18\}\\\\1.\ D\ \cap\ E=\{1;\ 4;\ 9;\ 16;\ 25;\ 36;\ 49;\ 64;\ 81\}=E\\conclusion\ E\subset D\\\\2.\ D\ \cap\ F=\{12;\ 14;\ 16;\ 18\}=F\\conclusion\ F\subset D\\\\3.\ D\ \cap\ (E\ \cap\ F)=D\ \cap\ \{16\}=\{16\}\\conclusion\ (E\ \cap\ F)\subset D\\\\4.\ D\ \cup\ (E\ \cap\ F)=D\ \cup\ \{16\}=\{0;\ 1;\ 2;\ 3;\ 4;...\}=D\\conclusion\ (E\ \cap\ F)\subset D[/tex]

[tex]5.\ D\ \cap\ (E\ \cup\ F)\\=D\ \cap\ \{1;\ 4;\ 9;\ 12;\ 14;\ 16;\ 18;\ 25;\ 36;\ 49;\ 64;\ 81\}\\=\{1;\ 4;\ 9;\ 12;\ 14;\ 16;\ 18;\ 25;\ 36;\ 49;\ 64;\ 81\}=E\ \cup\ F\\conclusion\ E\ \cup\ F\subset D[/tex]

D∩E = E

D∩F = F

D∩(E∩F) = {16}

DU(E∩F) = D

D∩(EUF) = {1,,4,9,12.14,16,18,35,36,47,64,81}

Given,

D = {x | x is a whole number}.

E = {x | x is a perfect square < 100}.

F = {x | x is an even number between 10 and 20}.

We are to find the following:

1. D ∩ E

2. D ∩ F

3. D ∩ (E ∩ F)

4. D ∪ (E ∩ F)

5. D ∩ (E ∪ F)

What are the different types of set's functions?

The intersection between two sets is denoted by ∩.

This means common values between the sets considered.

Union of two sets denoted by U.

This means all values from all the sets considered.

We have,

D = {x | x is a whole number}

D = {0,1,2,3,4,5,6,7,8,.........}

E = {x | x is a perfect square < 100}

E = {1,,4,9,16,35,36,47,64,81}

F = {x | x is an even number between 10 and 20}

F = {12,14,16,18}

Now,

D∩E = The common values from set D and E

        = E (all perfect square < 100 )

D∩F = F

This means all even number between 10 and 20}

D∩(E∩F) = {16}

E∩F = {16}

The only value common to both set D and E∩F is 16.

DU(E∩F) = D ( This means all whole numbers)

E∩F = {16}

D∩(EUF) = {1,,4,9,12.14,16,18,35,36,47,64,81}

EUF = {1,,4,9,12.14,16,18,35,36,47,64,81}

Thus the values are:

D∩E = E

D∩F = F

D∩(E∩F) = {16}

DU(E∩F) = D

D∩(EUF) = {1,,4,9,12.14,16,18,35,36,47,64,81}

Learn more about sets functions here:

https://brainly.com/question/11427505

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