write \\(subseteq\\) or \\(\nsubseteq\\) in each blank so that the resulting statement is true.\\({x|x\\text{…

write \\(subseteq\\) or \\(\nsubseteq\\) 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\\)\\(\nsubseteq\\)

write \\(subseteq\\) or \\(\nsubseteq\\) 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\\)\\(\nsubseteq\\)

Answer

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:

$\nsubseteq$