If I had two ciphertexts
$$c_1 = m_1 \oplus y_1 \text{ and } c_2 = m_2 \oplus y_2$$
will it be possible to obtain
$$z_1= (m_1 \lor m_2) \oplus y_1 \oplus y_2 \text{ and } z_2= (m_1 \land m_2) \oplus y_1 \oplus y_2$$
from $c_1$ and $c_2$ without revealing $m_1$, $m_2$, $y_1$ and $y_3$?