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Show that the following four conditions ...

Show that the following four conditions are equivalent :
(i) A ⊂ B (ii) A – B = Φ (iii) A ∪ B = B (iv) A ∩ B = A

Answer

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Match the following : (b)(ii)

Consider the sets φ, A = { 1, 3 }, B = {1, 5, 9}, C = {1, 3, 5, 7, 9} . Insert the symbol ⊂ or ⊄ between each of the following pair of sets: (i) φ . . . B (ii) A . . . B (iii) A . . . C (iv) B . . . C

Knowledge Check

  • Let A= {a,b,c}. Which of the following is not an equivalence relation in A?

    A
    `R_(1)= {(a,b),(b,c),(a,c),(a,a)}`
    B
    `R_(2)= {(c,b),(c,a),(c,c),(b,b)}`
    C
    `R_(3)= {(a,b),(b,b),(c,c),(a,b)}`
    D
    None of these

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