We will show the sets are equal using the definition of set equality.
To show that a bi-implication is true, we have to prove both directions. So first suppose that \( x \in A \), then since \( A \subseteq B \), \( x \in B \). For the other direction suppose that \( x \in B \), then since \( B \subseteq A \) then \( x \in A \). Therefore we know that \( x \in A \) if and only if \( x \in B \) as needed.
note: The symbol for rationals can be remebered as they are \( \mathbb{Q} \)uotients
note: The symbol for integers can be remembered as the word for number in German is \( \mathbb{Z} \)ahlen