If Y = house, tree and V = cat, house, tree, which of the following is true of Y and V?

We are given two sets:
$Y = \{\text{house, tree}\}$
$V = \{\text{cat, house, tree}\}$

We need to determine which statement is true.

• For $Y = V$ to be true, both sets must contain exactly the same elements. $Y$ has "house" and "tree", while $V$ has "cat", "house", and "tree". Since $V$ contains "cat" which is not in $Y$, $Y \neq V$. So, option A is false.
• For $Y \subset V$ (Y is a proper subset of V) to be true, every element of $Y$ must also be an element of $V$, and $V$ must contain at least one element not in $Y$. The elements of $Y$ are "house" and "tree". Both "house" and "tree" are present in $V$. The set $V$ contains "cat", which is not in $Y$. Therefore, $Y$ is a proper subset of $V$. So, option B is true.
• For $V \subset Y$ (V is a proper subset of Y) to be true, every element of $V$ must also be an element of $Y$, and $Y$ must contain at least one element not in $V$. The element "cat" is in $V$ but not in $Y$. Therefore, $V$ is not a subset of $Y$. So, option C is false.
• For $V \in Y$ (V is an element of Y) to be true, the entire set $V$ must be one of the items listed inside the curly braces of $Y$. The elements of $Y$ are "house" and "tree", not the set $V$. So, option D is false.

Based on the analysis, the statement $Y \subset V$ is true.

The correct option is B.
$\boxed{\text{B. } Y \subset V}$