1 1 vote If A, B, C are three sets then which of the following is TRUE ? If ( A ∩ C ) = ( B ∩ C ) then A = B If ( A ∪ C ) = ( B ∪ C ) then A = B If ( A 𝜟 C ) = ( B 𝜟 C ) then A = B If ( A – C ) = ( B – C ) then A = B Set Theory & Algebra set-theory&algebra set-theory discrete-mathematics + – pranay91331 1.5k views answer comment Share Follow Print See all 4 Comments 4 4 Comments reply sakharam commented May 10, 2019 reply Follow flag Counter examples for 1) A={1,2,3} B={4,5,6} C={7,8,9} Here ( A ∩ C ) = ( B ∩ C ) =$\phi$ but A != B 2) A={1,2} B={3,4} C={1,2,3,4,5} Here ( A ∪ C ) = ( B ∪ C ) ={1,2,3,4,5} but A != B 4) A={1,2,3} B={1,2,3,4} C={3,4} Here ( A – C ) = ( B – C ) ={1,2} but A != B 2 2 replyShare sakharam commented May 10, 2019 reply Follow flag Proof for 3rd: https://math.stackexchange.com/questions/1871160/a-delta-c-b-delta-c-then-prove-that-a-b-where-delta-is-a-symmetric 2 2 replyShare pranay91331 commented May 10, 2019 reply Follow flag Option 3 is the given answer. 0 0 replyShare sakharam commented May 10, 2019 reply Follow flag Yes that's right I gave counter example for 1,2 and 4 and the proof for 3rd about why it is true. 0 0 replyShare Please log in or register to add a comment.
0 0 votes No option is correct. Maguluri Bhaskar answered May 14, 2020 Maguluri Bhaskar comment Share Follow 0 reply Please log in or register to add a comment.
