Suppose that n and m are positive integers, and P, Q, P1,...,,Pn, Q1,...Qm are statements such that:

i. P logically follows from P1,...,Pn. In other words, if we have premises P1,...,Pn, then P follows as a conclusion.

ii. Similarly, Q logically follows from Q1,...,Qm.

Is it true that the conjunction (P and Q) follows from P1,...,Pn, Q1,...,Qm?

In other words, if we have premises P1,...,Pn, Q1,...,Qm, does (P and Q) follow as a conclusion?