Question

write \\(subseteq\\) or \\(
subseteq\\) in each blank so that the resulting statement is true.\\({x|x\text{ is a dog}}______{x|x\text{ is a black dog}}\\{x|x\text{ is a dog}}\\{x|x\text{ is a black dog}}\\)

Explanation:

Step1: Define subset condition

A set $A \subseteq B$ iff every element of $A$ is in $B$.

Step2: Analyze the two sets

Let $A=\{x|x \text{ is a dog}\}$, $B=\{x|x \text{ is a black dog}\}$. There exist dogs (e.g., a white dog) in $A$ that are not in $B$. So $A$ is not a subset of $B$.

Answer:

$
subseteq$