  Parity violating asymmetry in inclusive scattering of longitudinally
polarized electrons by unpolarized protons with $\pi^0$ or $\pi^+$ meson
production, is calculated as a function of the momentum transfer squared $Q^2$
and the total energy $W$ of the $\pi N$-system. This asymmetry, which is
induced by the interference of the one-photon exchange amplitude with the
parity-odd part of the $Z^0$-exchange amplitude, is calculated for the
$\gamma^*(Z^*)+p\to N+\pi$ processes ($\gamma^*$ is a virtual photon and $Z^*$
a virtual Z-boson) considering the $\Delta$-contribution in the $s-$channel,
the standard Born contributions and vector meson ($\rho$ and $\omega$)
exchanges in the $t-$channel. Taking into account the known isotopic properties
of the hadron electromagnetic and neutral currents, we show that the P-odd term
is the sum of two contributions. The main term is model independent and it can
be calculated exactly in terms of fundamental constants. It is found to be
linear in $Q^2$. The second term is a relatively small correction which is
determined by the isoscalar component of the electromagnetic current. Near
threshold and in the $\Delta$-region, this isoscalar part is much smaller (in
absolute value) than the isovector one: its contribution to the asymmetry
depend on the polarization state (longitudinal or transverse) of the virtual
photon.
