SOLUTION
Given the question in the question tab, the following are solution steps to get the elements of B that belong to the given set.
Step 1: Define rational numbers
A rational number is a number that can be expressed in the form of p/q, where p and q are integers and q is not equal to 0. Non-terminating decimals that do not have repeated numbers after the decimal point are not rational numbers.
Step 2: Write out the given sets
[tex]\begin{gathered} B=\mleft\lbrace20,\sqrt[]{8,}-6,0,\frac{0}{9},0.3\mright\rbrace \\ Rational\text{ numbers=}\times\mleft\lbrace\frac{p}{q}\mright|p,q\text{ are real numbers},and\text{ q}\ne0\} \end{gathered}[/tex]Step 3: Write out the rational numbers from set B
[tex]\begin{gathered} 20\text{ }\epsilon Rational\text{ numbers (because it can be written in the }\frac{p}{q}\text{ as in }\frac{20}{1}) \\ \sqrt[]{8}\text{ is not a rational number because the solution gives a non-terminating decimal with non repeating digits} \\ -6\text{ }\epsilon Rational\text{ numbers (because it can be written in the }\frac{p}{q}\text{ as in }\frac{-6}{1}) \\ 0\text{ }\epsilon Rational\text{ numbers (because it can be written in the }\frac{p}{q}\text{ as in }\frac{0}{1}) \\ \frac{0}{9}\text{ }\epsilon Rational\text{ numbers (because it can be written in the }\frac{p}{q}\text{ }) \\ 0.3\text{ }\epsilon Rational\text{ numbers (because it can be written in the }\frac{p}{q}\text{ as in }\frac{3}{10}) \end{gathered}[/tex]Hence, it can be seen from the explanations in Step 3 that the following are rational numbers:
Option B:
[tex]\lbrace20,-6,0,\frac{0}{9},0.3\rbrace[/tex]