Question

8) Prove that the P(XY) = P(X) ? P(Y). Note half of this proof was done in class. 9) Let X, Y and Z be sets. Prove that if XOY-XOZ then XYCZ 10) Prove or disprove. For any set A and B either AC Bor BCA.

          8) Prove that the P(XY) = P(X) ? P(Y). Note half of this proof was done in class.
9) Let X, Y and Z be sets. Prove that if XOY-XOZ then XYCZ
10) Prove or disprove. For any set A and B either AC Bor BCA.

Added by Nathan C.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Jill Tolbert

Step 1

To prove this, we need to show two inclusions: \( P(XY) \subseteq P(X) \cap P(Y) \) and \( P(X) \cap P(Y) \subseteq P(XY) \). Step 1.1: Show \( P(XY) \subseteq P(X) \cap P(Y) \). Let \( S \in P(XY) \). This means \( S \subseteq XY \). Since \( XY \subseteq X \) Show more…

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8) Prove that the P(rox) âŠ† P(Y). Note half of this proof is done. class 9) Let X and Y be sets. Prove that if X âŠ† Y, then X âˆ© Z âŠ† Y âˆ© Z. 10) Prove or disprove. For any sets A, B, and C, if A âŠ† B and B âŠ† C, then A âŠ† C.