Given two sets X and Y, if X is a proper subset of Y must X be a smaller set than Y? Explain.?

Question

Given two sets X and Y, if X is a proper subset of Y must X be a smaller set than Y? Explain.?

Answer 1

being a subset means it qualifies something else

for example if Y means mammal and X means Dog, X is a subset because it further qualifies "mammal" down to a certain group, in this case "dogs"

Answer 2

A proper subset is always smaller than its superset, so yes.  A subset is a set which has all of its elements appear in another set, called the superset.  A proper subset is a subset that does not have all the members of the superset.  For example,

X = { 1, 3, 9 }

Y = {1, 3, 5, 7, 9 }

Z = { 1, 3, 9 }

X is a proper subset of Y.  Z is also a proper subset of Y.  X can be considered a subset of Z because every element in X also appears in Z, but X is not a proper subset of Z because every element also appears in X; in other words they are equal.