A={1,2,3},B={1,2,2,3}. Is B⊆A? And is B⊂A? I was thinking yes to the first question and no to the second. They are equal sets right even though B has duplicate elements.
 A: $$A=B$$
So yes to the first and no to the second.
Don't worry about the duplicates. When we're talking about sets, only the existence matter and not how many times. Sets that counts how many times it appears are referred as multisets.
A: The article on multisets on wiki is of interest:

In mathematics, a multiset (or bag, or mset) is a modification of the
concept of a set that, unlike a set, allows for multiple instances for
each of its elements. The positive integer number of instances given
for each element is called the multiplicity of that element in the
multiset. As a consequence, an infinite number of multisets exist
which contain only elements a and b, but vary in the multiplicities of
their elements:
The set {a, b} contains only elements a and b, each having multiplicity 1 when {a, b} is seen as a multiset.
In the multiset {a, a, b}, the element a has multiplicity 2, and b has multiplicity 1.
In the multiset {a, a, a, b, b, b}, a and b both have multiplicity 3.
These objects are all different, when viewed as multisets, although
they are the same set, since they all consist of the same elements. As
with sets, and in contrast to tuples, order does not matter in
discriminating multisets, so {a, a, b} and {a, b, a} denote the same
multiset

And later in the page :

Inclusion: A is included in B, denoted A ⊆ B, if
$\forall x\in U, m_A(x)\le m_B(x)$

Therefore seen as sets then $A=B$ and seens has multisets since $m_A(2)=1\le m_B(2)=2$ and other multiplicities are the same, then $A\subset B$ and $A\neq B$.
