Post a New Question

maths

posted by .

Let A, B and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C.

Show that B = C.

  • maths -

    you can easily prove oit with a Venn diagram.
    If not: A¾B=A+B-A¿B=A+B-A¿C
    AUC=A+C-A¿C
    As AUB=AUC then A+B-A¿C=A+C-A¿C hence; B=C

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    1) Given the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and sets A = {2, 3, 4, 6}, B = {5, 6, 7, 8, 10}, C = {6, 8, 10}, and D = {1, 2, 7, 9}, answering the following: 1- a) What is A ∪ C?
  2. maths

    Let A, B and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. Show that B = C.
  3. probability

    PROBLEM 2: SET OPERATIONS AND PROBABILITIES (3 points possible) Find the value of P(A∪(Bc∪Cc)c) for each of the following cases: The events A, B, C are disjoint events and P(A)=2/5. P(A∪(Bc∪Cc)c)= incorrect …
  4. discrete math help please

    1. for any sets X and Y, we define the symmetric difference X ∆Y by: X∆Y = (X - Y) ∪ (Y - X) = (X ∪ Y) - (X ∩ Y) Prove the following: -for all sets A,B and C, if A - (B ∩ C) = ∅ then A- C ⊆ …
  5. discrete math help please

    1. for any sets X and Y, we define the symmetric difference X ∆Y by: X∆Y = (X - Y) ∪ (Y - X) = (X ∪ Y) - (X ∩ Y) Prove the following: -for all sets A,B and C, if A - (B ∩ C) = ∅ then A- C ⊆ …
  6. URGENT! discrete math help please

    1. for any sets X and Y, we define the symmetric difference X ∆Y by: X∆Y = (X - Y) ∪ (Y - X) = (X ∪ Y) - (X ∩ Y) Prove the following: -for all sets A,B and C, if A - (B ∩ C) = ∅ then A- C ⊆ …
  7. URGENT HELP WITH DISCRETE MATH PLEASE

    1. for any sets X and Y, we define the symmetric difference X ∆Y by: X∆Y = (X - Y) ∪ (Y - X) = (X ∪ Y) - (X ∩ Y) Prove the following: -for all sets A,B and C, if A - (B ∩ C) = ∅ then A- C ⊆ …
  8. Somebody please help urgently!

    1. for any sets X and Y, we define the symmetric difference X ∆Y by: X∆Y = (X - Y) ∪ (Y - X) = (X ∪ Y) - (X ∩ Y) Prove the following: -for all sets A,B and C, if A - (B ∩ C) = ∅ then A- C ⊆ …
  9. math. Somebody help urgently please

    1. for any sets X and Y, we define the symmetric difference X ∆Y by: X∆Y = (X - Y) ∪ (Y - X) = (X ∪ Y) - (X ∩ Y) Prove the following: -for all sets A,B and C, if A - (B ∩ C) = ∅ then A- C ⊆ …
  10. Math - sets

    Suppose A, B, and C are sets. In at least one of the following situations, one can conclude that A = B. Identify those cases where this conclusion does apply. (i) A ∪ C = B ∪ C A={1,2},A={1,2}, B={2,3}B={2,3} and C={1,2,3}.C={1,2,3}. …

More Similar Questions

Post a New Question