Question

Check whether the following statement is true or not.
If
x
,
y
∈
Z
are such that
x
and
y
are odd, then
xy
is odd.

Answer 1

Where are you getting these? LOL

Answer 2

@Noemi95

Answer 3

Suppose \[\huge x,y \in \mathbb{Z}\]
such that both x and y are odd...
then there exist integers...\(\large h,k \in \mathbb{Z}\)
such that
\[\Large x = 2h+1\\\Large y = 2k+1\]
Having said that...
\[\Large xy = (2h+1)(2k+1) =4hk+2(h+k)+1\]
\[\Large xy=2(\color{blue}{2hk+h+k})+1\]
Since h and k are integers,
\[\Large \color{blue}{2hk+h+k}\in \mathbb{Z}\]And therefore
xy is odd
∎