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Can someone please explain step by step the following solution. i am going to post the...

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Advance Math

Can someone please explain step by step the following solution.i am going to post the solution i just need someone to pleaseexplain why each step is taking and what formula is being used.please explain it to me thank tyou

Suppose A is a set and {Bi | i ? I} is an indexed family of setswith I ??.

  1. Prove that A ( ?i?I Bi ) = ?i?I (A Bi).
  • A be a set
  • Bi | i ? I} is an indexed family of sets with I ??
  • Let x?A - ?i?I Bi
  • => x?A & x??i?I Bi
  • => x?A & x? Bi for each i?I
  • => x?A - Bi for each i?I
  • => x? ?i?I (A - Bi)
  • so A - ( ?i?I Bi ) = ?i?I (A Bi) proven
  1. Interpret this theorem when I = {1, 2}.
  • To show that A-(B1?B2)=(A-B1)?(A-B2)
  • Let y?A - (B1?B2)
  • => y?A & y? B1?B2
  • => y?A & y? B1 & y?B2
  • => y?A & y? B1 & y?A &y?B2
  • => y?A - B1 & y?A - B2
  • => y? (A - B1) ? y? (A - B2)
  • so our claim is justified and hence the proof.

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