3 votes 3 votes When is the following statement true? (A ∪ B) ∩ C = A ∩ C (A) If Ā ∩ B ∩ C = φ (B) If A ∩ B ∩ C = φ (C) always (D) never Set Theory & Algebra jest discrete-mathematics set-theory&algebra + – sripo asked Feb 15, 2019 • retagged Mar 11, 2019 by Naveen Kumar 3 sripo 821 views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply Prateek Raghuvanshi commented Feb 15, 2019 reply Follow Share option B is the right answer only this van diagram satisfying the condition means intersection of three is nothing. 0 votes 0 votes Shaik Masthan commented Feb 15, 2019 reply Follow Share in general, (A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C) But in our question, (A ∪ B) ∩ C = A ∩ C ==> (B ∩ C) should be equal to ∅ then why not option A ? @Prateek Raghuvanshi 0 votes 0 votes Naveen Kumar 3 commented Feb 15, 2019 reply Follow Share ( A ∪ B) ∩ C = A ∩ C either A ∪ B =A ------(i) {either A=B or B is within A} or B ∩ C = ∅ -------(ii) if only case (i) will apply then, Ā ∩ B ∩ C = (Ā ∩ B) ∩ C = ∅ ∩ C = ∅ A ∩ B ∩ C = A ∩ C or A ∩ B ∩ C if only case (ii) or both cases apply then, B ∩ C=∅ =>Ā ∩ B ∩ C=A ∩ B ∩ C= ∅ so, option A is following always! correct if anywhere I'm wrong or you see any other case 3 votes 3 votes Please log in or register to add a comment.
0 votes 0 votes Option A Ram Swaroop answered Feb 15, 2019 Ram Swaroop comment Share Follow See all 0 reply Please log in or register to add a comment.