Prove the following, for sets A, B, C (i) `AsubeB,BsubeC=>AsubeC` (ii) `AsubeBiffAuuB=B,AsubeBiffAnnB=A`

Prove the following : (i) B-A=BcapA^(c) (ii) (AuuB)-A=B-A .

Prove that : (i) A sube B,B sube C rArrA sube C (ii) A sube phi, hArr A = phi

Prove that : (i) A sube B,B sube C rArrA sube C (ii) A sube phi, hArr A = phi

Prove that: AsubeB iff B'subeA'

If AsubeB and BsubeC then show that AsubeC .

For non-empty subsets A,B and C of a set X such that AuuB= BnnC, which one of the following, is the strongest inference that can be derived? a)A=B=C b) AsubeB=C c) A=BsubeC d) AsubeBsubeC

Prove that AsubeB,BsubeCandCsubeArArrA=C=B .

For any two sets A and B, prove that : (i) (A-B)cupB=AcupB (ii) (A-B)capB=phi

If A and B are two sets, then prove that : (i) (A-B)cupB=AhArrB subeA (ii) A subA cupB .

For any two sets A and B, prove that : (i) (A capB)cup(A-B)=A (ii) A cup(B-A)=A cupB .