Given: 1. If x is directly proportional to z and y is directly proportional to z, then (x2−y2) is directly proportional to z2. 2. If x is inversely proportional to z and y is inversely proportional to z, then ( xy ) is inversely proportional to z2 Calculation Case I. According to the question x∝z and y∝z ⇒x=zk and y=rz where k and r are constants ⇒x2=z2k2 and y2=r2z2⇒x2−y2=z2(k2−r2) ⇒x2−y2∝z2 Hence, Case I is correct. Case II. x∝1∕z and y∝1∕z ⇒xz=k and yz=r where k and r are constants ⇒xz.yz=kr ⇒xyz2=kr ⇒xy=kr∕z2 ⇒xy∝1∕z2 Hence, Case II is correct.