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}}\\)\\(subseteq\\)\\(
subseteq\\)

Explanation:

Step1: Define set inclusion

A set $A \subseteq B$ if every element of $A$ is an element of $B$.

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) that are in $A$ but not in $B$. So $A$ is not a subset of $B$.

Answer:

$
subseteq$