I assume the set A referred to among all the answer choices is actually supposed to be B, or the other way around so that
A = {1, 2, 3, {4, 5, 6, {7}}, 8}
A has <u>5</u> elements:
• 1
• 2
• 3
• {4, 5, 6, {7}}
• 8
Any non-empty subset of A is a set containing at least one of these elements.
The fourth element listed above, {4, 5, 6, {7}}, is itself a set with 4 elements (4, 5, 6, and yet another set {7} that contains just the 1 element 7).
Now,
• { } ⊆ A is true - the empty set is subset of every set
• {2, 3} ⊆ A is true - both 2 and 3 are elements of A, so {2, 3} is a subset of A
• {4, 5, 6, {7}} ⊆ A is false - the set {4, 5, 6, {7}} is an element of A, but not a subset
• {{2, 3}} ⊆ A is false - 2 and 3 are elements of A, but the set {2, 3} is not an element of A, so {{2, 3}} is not a subset
• {{4, 5, 6}, 8} ⊆ A is false - the set {4, 5, 6} is not an element of A
• {{4, 5, 6, {7}}} ⊆ A is true - the set {4, 5, 6, {7}} is an element of A
