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 membership

Let $A = \{x|x \text{ is a dog}\}$, $B = \{x|x \text{ is a black dog}\}$.

Step2: Analyze subset condition

A set $A \subseteq B$ iff every element of $A$ is in $B$. There exist dogs that are not black, so not all elements of $A$ are in $B$.

Answer:

$
subseteq$