Under the exchange of particle, the state of Fermions and Bosons are anti symmetric and symmetric respectively. For example, if $\psi_1(x)$ and $\psi_2(x)$ are two one particle wavefunctions, two particle Fermionic and Bosonic wavefunctions are [not normalized] $$\psi_1(x_1)\psi_2(x_2)-\psi_1(x_2)\psi_2(x_1) \hspace{1cm} Fermionic$$ $$\psi_1(x_1)\psi_2(x_2)+\psi_1(x_2)\psi_2(x_1) \hspace{1cm} Bosonic$$
What will be the wavefunction of a two particle system consists of one Fermion and one Boson? Will it retain any symmetry property?