Question

Can anyone walk me step by step through this?

Answer 1

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 5 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