ID: 339
Verify the correctness of the given statement. "For all integers j and k, if j and k are odd, then jk is odd."
Aligned LLM's Response:
Thank
you
for
asking
!
The
statement
you
provided
is
actually
false
.
\n
The
statement
"
For
all
integers
j
and
k
,
if
j
and
k
are
odd
,
then
j
k
is
odd
"
is
not
true
.
\n
To
see
why
,
consider
the
following
counter
example
:
\n
Let
j
=
3
and
k
=
5
.
Both
j
and
k
are
odd
,
but
j
k
=
1
5
is
even
.
\n
So
,
the
statement
is
not
univers
ally
true
,
and
it
is
important
to
be
careful
when
making
claims
about
the
properties
of
integers
.
\n
I
hope
this
helps
clarify
things
!
Let
me
know
if
you
have
any
other
questions
.
</s>
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