If X and Y are two sets of vectors in a vector space V, and if X $\subset$ Y, then is span X $\subset$ span Y?

Question

If X and Y are two sets of vectors in a vector space V, and if X $\subset$ Y, then is span X $\subset$ span Y? If so, why is or isn't the span of X a subset of the span of Y?

EDIT:

Thank you for the hints!
Here is the proof I came up with; please let me know if it is correct.

The spanning set of X can be written as:
Span(X) = {$a_1 x_1 + a_2 x_2 + ... + a_n x_n$} where all $x_i$ are vectors and all $a_i$ are scalars.
Since X$\subset$Y then all $x_i$ are also in Y.
Thus, Span(x) is a linear combination of vectors from Y
So Span(x) $\subset$ Span(Y).

Answer 1

Hint:

Every linear combination of elements of $X$ is also a linear combination of elements of $Y.$

Answer 2

Hint: A linear combination of elements in $X$ is already a linear combination of elements in $Y$.