Thread: Problem 1, Section 1...:(

Explain why .

Originally Posted by VonNemo19

Explain why .

Is this a trick question?
What don't understand about it? Do you know the symbols involved?

Originally Posted by Plato

Is this a trick question?
What don't understand about it? Do you know the symbols involved?

I got it. I had to read the section again.

In particular:

"According to cantor, a set is made up of objects called members or elements...If the first blank in '_____ is a member of _____' is filled in with the name of an object, and the second with the name of a set, the resulting sentence can be classified as either true or false."

So, I guess the answer is

Because is a true statement.

Right?

Explain why

Because is a true statement.

The questions "Why ?" and "Why '' is a true statement" are, in fact, one and the same. If somebody asks you, "Why are you late?", it does not make sense to answer "Because 'I am late' is a true statement".

Originally Posted by emakarov

The questions "Why ?" and "Why '' is a true statement" are, in fact, one and the same. If somebody asks you, "Why are you late?", it does not make sense to answer "Because 'I am late' is a true statement".

So, what would you say they are looking for here?

I am also not sure about exact words for such a trivial case, but I would say, because 2 is listed as an element of the set. That's why it belongs.

Unless it's advanced math, the concepts of a set, an element and belonging are taken as primitive.

Originally Posted by VonNemo19

Explain why .

Here is the proof:

.

Since

Hello at all!

Here is a formal proof for the statement:

1) .................................................. .................................................. .law of identity
2) .................................................. .................................................. ............1, Universal Elimination, where we put
3) .................................................. .................................................. ....2, Disjunction Introduction
4) .................................................. .................................................. ....3, Commutation equivalence
5) .................................................. ...........theorem of set theory
6) .................................................. ......................5, Universal Elimination, where we put , and
7) .................................................. ..........................6, Biconditional Elimination
8) .................................................. .................................................. ...4, 7, Modus Ponens
9) .................................................. ......................................8, Disjunction Introduction
10) .................................................. ....theorem of set theory
11) .............................................10, Universal Elimination, where we put , and
12) .................................................1 1, Biconditional Elimination
13) .................................................. ..........................................9, 12, Modus Ponens
14) .................................................. ........definition of triplet set
15) .................................................. .....................................14, Universal Elimination, where we put , and
16) ............................axiom of extensionality
17) ..............16, Universal Elimination, where we put and
18) ..............17, Biconditional Elimination
19) ................................................15 , 18, Modus Ponens
20) .................................................. ........19, Universal Elimination, where we put
21) .................................................. ............20, Biconditional Elimination
22) .................................................. .................................................. 13, 21, Modus Ponens

Best wishes,
Seppel