Number of non-empty subsets of A=2m−1 Number of non-empty subsets of B=2n−1 ∴2m−1=2k+2n−1 ⇒2m=2k+2n When m=n+2 2n+2=2k+2n⇒2n(4−1)=2k ⇒3=2k−n,which is not possible as LHS is odd and RHS is even. When m=n+1 2n+1=2k+2n⇒2n(2−1)=2k ⇒2n=2k,which is possible when n = k. When m=n+p 2n+p=2k+2n⇒2n(2p−1)=2k ⇒2p−1=2k−n,which is not possible as LHS is odd and RHS is even When m=n+t 2n+t=2k+2n⇒2n(2t−1)=2k ⇒2t−1=2k−n,which is not possible as LHS is odd and RHS is even. Trick : Take m=2,n=2 Then,23−1=7=22+(22−1) ⇒m=n+1