Please help me with this.Use element argument to prove the statement. Assume that all sets are subsets of a universal set U, Statement: For all sets A, B, and C, A ∩ (B − C) = (A ∩ B) − (A ∩ C). Please do the proof like the way the example proof does it. Thanks. 10. Proof: Suppose A, B, and C are any sets.We will show that (A U B) N CCAU(BN C).Suppose x is any element (A U B) N C.By definition of intersection x is in A U Band x is in C.Then by definition of union x is in A or x is in B, andin both cases x is in C. It follows by definition ofunion that in case x is in A and x is in C, then x is inAU (B N C) by virtue of being in A. And in case x isin BN C, then x is in A U (B NC) by virtue of beingin BN C. Thus in both cases x is in A U (BN C),which proves that every element in (A U B) N C is inAU (B N C).Hence (A U B) nCCAU(BNC) by definition ofsubset.

The given statement is 'for all sets A, B, and C, A ∩ (B − C) = (A ∩ B) − (A ∩ C).'

Use element argument to prove the statement. Assume that all sets are subsets of a universal set U, Statement: For all sets A, B, and C, A ∩ (B − C) = (A ∩ B) − (A ∩ C). Please do the proof like the way the example proof does it. Thanks.

Use element argument to prove the statement. Assume that all sets are subsets of a universal set U, Statement: For all sets A, B, and C, A ∩ (B − C) = (A ∩ B) − (A ∩ C). Please do the proof like the way the example proof does it. Thanks.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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