Not a superset of

It denies that A contains B as a superset. A set is a collection of objects, called elements. A superset contains every element of the other set; a strict or proper superset also contains something extra. The slash in ⊅ means “not.”

For example, let A = {1, 2} and B = {2, 3}. A ⊅ B is true because 3 belongs to B but not A. The sets still share 2: this symbol does not say they have nothing in common.

What if the two sets are equal?

Equality depends on how the text defines ⊃. If ⊃ means “strict superset,” A ⊅ B is true when A = B: A has no extra element. If ⊃ allows equality, A ⊅ B is false when A = B.

The more explicit ⊉ negates “superset or equal to.” A ⊉ B means that at least one element of B is missing from A, so it is always false for equal sets. Check your textbook's notation before treating ⊅ and ⊉ as interchangeable.