For two events A and B it is given that P(A) = 0.6 and P(B) = 0.5. Which statement MUST be true?

If the two events could never happen together then P(A or B) would be 0.6 + 0.5 = 1.1, and no probability may exceed 1. So they must overlap, and rearranging P(A or B) = P(A) + P(B) − P(A and B) ≤ 1 shows P(A and B) ≥ 0.1. Nothing in the question forces independence — P(A and B) = 0.30 is possible but not compelled, and any value from 0.1 to 0.5 would do. The two options that call the events mutually exclusive both rest on an impossible total.