Question

Let A be the following set. A = {∅, 1, {1,2}}. Mark each of the following true or false.
1. {∅}∈P(A)
2. {∅,1}∈P(A)
3. (1,2)∈A×A
4. {{1,2}}∈P(A)
5. {∅,1}∈A×A

Answer 1

how far did you get?

Answer 2

1. false
2. true
3. false
4. true
5. true

That's what I got and it says I'm 60% correct so two of these are wrong but I'm not sure which ones. The set inside the set is throwing me off a little

Answer 3

P(A) means the powerset of A

the powerset is the set of all subsets of a given set. The powerset of A is this set

{
∅
{∅}, {1}, {{1,2}}
{∅,1}, {∅,{1,2}}, {1,{{1,2}}
{∅, 1, {1,2}}
}

Answer 4

based on this, we can see that {∅} is an element of P(A)

so 1 is true

Answer 5

2. {∅,1}∈P(A) is also true for the same reason

Answer 6

3. (1,2)∈A×A is false because 1 is an element of A, but 2 is not

Answer 7

4. {{1,2}}∈P(A is true for the same reasons as 1 and 2

Answer 8

5. {∅,1}∈A×A is false beacuse it should be (∅,1) and NOT {∅,1}

you need an ordered pair

Answer 9

because*