Question 187192
False

There are many A ⊆ B. Any proper subset of B will be missing at least one element of B. So, in your problem, if 'b' is one of the elements that is 'left out of the subset', then b ∈ B  but not an ∈ of A

As an example, assume B = {1, 2, 3, 4}
Let A = {1,2}. In this case both 3 and 4 are ∈ B. While neither is ∈ A