Express the following as a precise mathematical statement:

The product of two integers with different parity is always odd.

If $x,$yinZ such that $x=2$a and $y=2b+1$ for some $a,$binZ, then $xy=2c+1$ for some cinZ.

If $x,$yinZ such that $x=2k$ and $y=2k+1$ for some kinZ, then $xy=2k+1.$

If xinZ such that $x=2n$ and yinZ such that $y=2m+1,$ then xyinZ such that $xy=2p+1.$

If $x=2n$ and $y=2n+1$ for some ninZ, then $xy=2k+1$ for some kin E z