Question
Show how a contradiction arises from the following taken as an assumption (∃y)(x)(x∈y≡∼(x∈x))
Show how a contradiction arises from the following taken as an assumption
(∃y)(x)(x∈y≡∼(x∈x))
Homework Answers
Answer #1
The assumption tells us that
The statement that there exists 
such that forall
,
belongs to is equivalent to the
statement is not contained in
.
The contradiction arises because the statement " is not contained in
" is
not true even if the statement "there exists such that forall
" is
true.
Consider the set of rationals 
.
Obviously there exists the set of reals 
such that
i.e. is contained
in but
is also contained in i.e. 
also holds.
Hence the assumption is wrong.
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