Question

Select the statements that are true based on the following given information. D = {x | x is a whole number} E = {x | x is a perfect square < 36} F = {x | x is an even number between 20 and 30} The expression D ∪ E = E. E ∪ (D ∩ F) is {25}. F ⊂ D (E ∩ F) is the empty set. Set E is infinite.

Answer 1

D = {x | x is a whole number} = { 0, 1, 2, 3, 4, 5, ...}

E = {x | x is a perfect square < 36} = { 0, 1, 4, 9, 16, 25}

F = {x | x is an even number between 20 and 30} = { 22, 24, 26, 28}

$D\ \cup\ E=D\neq E-FALSE\\\\E\ \cup\ (D\ \cap\ F)=E\ \cup\ F=\{0, 1, 4, 9, 16, 22, 24, 25, 26, 28\}\neq\{25\}-FALSE\\\\F\ \subset D-CORRECT\\\\E\ \cap\ F=\O-CORRECT\\\\E\ is\ infinite-FALS$

Answer 2

Answer:

D = {x | x is a whole number}

E = {x | x is a perfect square < 36}

F = {x | x is an even number between 20 and 30}

Set E is infinite.                    FALSE

F ⊂ D                                      TRUE  

(E ∩ F) is the empty set.      TRUE

E ∪ (D ∩ F) is {25}.                FALSE

The expression D ∪ E = E.  FALSE