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kenny6666 [7]
2 years ago
3

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}
Mathematics
2 answers:
irga5000 [103]2 years ago
7 0
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

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
Dmitrij [34]2 years ago
6 0

D ∩ E =  {1, 4, 9, 16, 25, 36, 49, 64, 81}

D ∩ F =  {12, 14, 16, 18}

D ∩ (E ∩ F) =  {16}

D ∪ (E ∩ F) =  {all whole numbers}

D ∩ (E ∪ F) =  {1, 4, 9, 16, 25, 36, 49, 64, 81, 12, 14, 18}

(These are correct.)

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