# key2fa00 - COT3100C-01, Fall 2000 S. Lang Solution Key to...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: COT3100C-01, Fall 2000 S. Lang Solution Key to Assignment #2 (40 pts.) 9/26/2000 1. (6 pts.) The following Venn diagram shows three sets A , B , and C contained within a universe set named U . In the diagram, different subsets (regions) are labeled by the numbers 1 through 8. Thus, set A contains subsets labeled 1, 2, 4, and 5; set B contains subsets labeled 2, 3, 5, and 6; set C contains subsets labeled 4, 5, 6, and 7; set U contains subsets labeled 1 through 8 (i.e., the universe). Now, give the labels (i.e., numbers) of the subsets that are contained in each of the following sets: 2. (24 pts.) Prove each of the following statements (a) – (f), assuming the symbols A , B , and C represent sets. You are allowed to use appropriate definitions, and the following theorems and laws ( but only these ) in the proof. Be sure to explain each step of your proof. (Commutative Law) A ∪ B = B ∪ A , A ∩ B = B ∩ A . (Associative Law) ( A ∪ B ) ∪ C = A ∪ ( B ∪ C ), ( A ∩ B ) ∩ C = A ∩ ( B ∩ C ). (Distributive Law) A ∪ ( B ∩ C ) = ( A ∪ B ) ∩ ( A ∪ C ) , A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C ) . (Idempotent Property) A ∪ A = A , A ∩ A = A . (De Morgan’s Law) ¬ ( A ∪ B ) = ¬ A ∩ ¬ B , ¬ ( A ∩ B ) = ¬ A ∪ ¬ B . (Double Negation) ¬ ( ¬ A ) = A . (Complementary Property) A ∩ ¬ A = ∅ , A ∪ ¬ A = U , where U denotes the universe....
View Full Document

## This document was uploaded on 06/09/2011.

### Page1 / 3

key2fa00 - COT3100C-01, Fall 2000 S. Lang Solution Key to...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online