Let X = {∅,{∅} },{0},2,3,,{4,5}}.Examine whether the following statements are true or false.?
1)…………… ∅ subset of P(X)
2)……………∈P(X)
3)……………{∅} ∈P(X)
4) ………………{{∅}} ∈ P(X)
5)……………..{2}∈P(X)
6)………………{{{4,5}}} is a subset of P(X)
7)……………..{{0},2} ∈ P(X)
8)……………..{{0},3} is a subset of the P(X)
9)……………..{{ ∅},∅} ∈ P(X)
10)…………….{{4,5},2} ∈P(X)
My answers are
1. T 4. F 7. T 10. T
2. F 5. T 8. F
3. F 6. T 9. F
I’m not sure of my answers especially number 6
Thanks a lot
Update:I think that {2} is a subset of X because 2 is an element and if you write it as a subset of x it becomes {2}. same as {4,5} is an element of X and it becomes {{4,5}} subset of X . how will i write the P(X), do i need to put three braces?
thnks a lot
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Answers & Comments
Verified answer
1. T
2. Don't know. Look's like you missed something.
3. Depending on the second element. Did you mean {∅} or {{∅}}? In the former case, T. In the latter case, F
4. Opposite of 3.
5. F. X does not contain {2}. It contains 2. They're different.
6. F. Element of {{{4,5}}} is {{4,5}} which is not an element of X.
7. F. X does not contain {{0}, 2}. It contains {0} and 2. Again, different.
8. T. Elements of {{0},3} are {0} and 3, both of which are contained in X.
9. F. Same reason as 7.
10. F. Same reason as 7.
Edit:
Oh shoot. It was P(x).. I thought it was just X. -_-;;; My apology
1. T
2. Still don't know
3. T. {∅} is subset of X, thus this is element of P(x)
4. T if second element is {∅}
5. T
6. T
7. T
8. F
9. T. {{∅}, ∅} is subset of X. So, it's element of P(x)
10. T
Once again, my apology.
Its fake. think of of it like this.......... if a = 2 and b =3 then (2+3)^2 =25 2^2 +3^2 =13 those are definately no longer equivalent and you will use different numbers in decision to a and b. An previous instructor I as quickly as had pronounced that the sum of the squares replaced into no longer equivalent to the sq. of the sum and that easy rule applies here CD