If `AxxBsubeCxxD` and `AxxB ne phi`, then show that, `AsubeC` and `BsubeD`.

If AsubeB and BsubeC then show that AsubeC .

If AleB show that A-B=phi

If AcapB'=phi , then show that A=AcapB and hence show that AsubeB .

If AcapB^1=phi ,then show that A=AcapB and hence show that AsubeB .

If A={0,1} and B={0,-1} then show that AxxB ne BxxA

show that (A-B)capB=phi

If two-empty sets A and B have n elements in common, then show that AxxB and BxxA have n^(2) elements in common.

Let QQ be the set of rational numbers, If f: QQ rarr QQ is defined by f(x)=ax+b , where a, b, x in QQ and a ne 0 , then show that f is invertible and hence find f^(-1)

Let A={x:x in ZZ wedge-1 ltx le 1}, B={x:x in NN wedge 1 lt x lt 5} and C={x:x is an odd positive integer x and 1ltx le6} , then show that, (AxxB) cup(AxxC) = Axx(BcupC)

If D is the mid-pointof the side BC of a triangle ABC and angleBAD = theta, angleCAD = phi , then show that cot theta - cot phi = cot B - cot C .