## (Solved) Writing Assignment #2 #1) Prove the following by using: a direct argument; the definition for union; the definition for intersection; and the...

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Prove the following by using: a direct argument; the definition for union; the definition for intersection; and the definition for set complement.Â

Writing Assignment #2
#1) Prove the following by using: a direct argument; the definition for union; the
definition for intersection; and the definition for set complement.
Let A , B , and U be sets. If U= A âˆª B and #2) Prove the following by using: a direct argument; and definition 2.1.16.
Consider practice problem 2.1.14 as an outline for your proof.
Let B { A j s . t . j âˆˆJ } be an indexed family of sets and let be a set. B âˆ© ( Â¿ jâˆˆ J A j ) =Â¿ j âˆˆ J ( B âˆ© A j )
#3) Prove the following by using: a direct argument; definition 2.2.9; definition of a
rational number; sum and product of integers are integers.
Let P y , i.e. be a relation on x P y , if xâˆ’ y R defined as: âˆ€ x , yâˆˆ R , x is related to is rational. #4) Prove the following by using: a contradiction argument; definition 2.3.1;
definition and notation 2.3.13; and Theorem 2.3.16.
Let f : Aâ†’B , S âŠ† A , and TâŠ†A . S âŠ†T

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