A and B are two sets containing respectively m1 and m2 elements. if X ≤ n (A U B) ≤ y, find x and y Share with your friends Share 0 Priyanka Kedia answered this If m1<m2We have nA∪B=nA+nB-nA∩B is minimum or maximum according to nA∩B is maximum or minimum. Case1: If nA∩B is minimum. i.e. nA∩B =0⇒ nA∪B=nA+nB-nA∩B ≥nA+nB ≥m1+m2 Case2: If nA∩B is maximum. i.e. nA∩B =m1⇒ nA∪B=nA+nB-nA∩B ≤nA+nB-m1 ≤m1+m2-m1 ≤m2Thus, m1+m2≤nA∪B≤m2And,If m1>m2We have nA∪B=nA+nB-nA∩B is minimum or maximum according to nA∩B is maximum or minimum. Case1: If nA∩B is minimum. i.e. nA∩B =0⇒ nA∪B=nA+nB-nA∩B ≥nA+nB ≥m1+m2 Case2: If nA∩B is maximum. i.e. nA∩B =m2⇒ nA∪B=nA+nB-nA∩B ≤nA+nB-m2 ≤m1+m2-m2 ≤m1Thus, m1+m2≤nA∪B≤m1 4 View Full Answer
