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Let me explain
1) Atleast one of P, Q and R is zero. We cannot determine how many are zeroes here. It could be 1 or 2 or 3 zeroes.
2) Sum of three numbers is zero
Here it is possible that P = -(Q+R) or Q = -(P+R) and none of them might be zero.
All can be zeroes. So this condition is insufficient. Here either none are zeroes or one is zero or three are zeroes
P = -(Q+R) here R might be zero which will satisfy A) then P = -Q which will satisfy B). So one zero will satisfy A and B
If All numbers are zero then also Both A) and B are satisfied.
So We cannot tell if there is one zer or three zeroes.