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Math Help - Need help proving!! Mathematical Induction

  1. #1
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    Need help proving!! Mathematical Induction

    Hey I'm struggling in Discrete Math, could anyone help me solve this proof?

    Prove that A1, A2, . . . ., An and B are sets, then (A1 ∩ A2 ∩ . . . ∩An) U B = (A1 U B) ∩ (A2 U B) ∩ . . . ∩(An U B).

    This comes from the Induction and Recursion chapter of Mathematical Induction.
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  2. #2
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    Quote Originally Posted by Saint22 View Post
    Hey I'm struggling in Discrete Math, could anyone help me solve this proof?

    Prove that A1, A2, . . . ., An and B are sets, then (A1 ∩ A2 ∩ . . . ∩An) U B = (A1 U B) ∩ (A2 U B) ∩ . . . ∩(An U B).

    This comes from the Induction and Recursion chapter of Mathematical Induction.
    Prove it by induction for n=2 we need to show (A_1\cap A_2) \cup B = (A_1 \cup B) \cap (A_2\cup B).
    This case is proven individually.

    If it is for (A_1\cap ... \cap A_n) \cup B = (A_1 \cup B)\cap ... \cap (A_n \cup B).

    Then if we have (A_1\cap ... \cap A_n \cap A_{n+1})\cup B = [(A_1\cap ... \cap A_n) \cap A_{n+1}] \cup B
    And this gives, (as in the case n=2):
    [(A_1\cap ... \cap A_n) \cup B] \cap (A_{n+1} \cup B)
    Now apply inductive step:
    (A_1\cup B)\cap ... \cap (A_{n+1} \cup B)
    And that completes induction.
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