99Se2 - 1 1a Prove Theorem 2.7g namely Let A and B be sets...

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

MARK BOX problem points 1 10 2 10 3 10 4 10 5 10 Total 40 % 100 Math 300X.001 Prof. Girardi Spring 99 Exam 2 4/6/99 NAME: INSTRUCTIONS : 1. Do 4 of the 5 problems. I am doing problem numbers: . 2. Use your own paper: a. write on only one side of the page b. begin each (numbered) problem on a new page c. put your name on each page d. put your pages in order. 3. For problems that request a proof, write a neat formal proof. 4. During this test, do not leave your seat. If you have a question, raise your hand. 5. This closed book/notes exam covers, from A Transition to Advanced Mathematics ,4 th Ch 2 . Problem Source : 1. from class lecture 2. from class lecture 3. hand-in problem 2.3 # 6b 4. Ch 2: Extra Practice Problems # 16 5. hand-in problem 2.5 # 2.

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: 1 1a. Prove Theorem 2.7g, namely: Let A and B be sets. Show that ( A ∩ B ) C = A C ∪ B C . 1b. Theorem 2.7g is commonly referred to as ’s Law. 2. Prove part of Theorem 2.5, namely: Let A and B be sets with A ⊆ B . Show that P ( A ) ⊆ P ( B ). hint : You may use, without proving, Theorem 2.2. 3. Let I = { A α : α ∈ Δ } be an indexed family of sets and let B be a set. Show that B [ \ α ∈ Δ A α ! = \ α ∈ Δ ± B [ A α ² . 4. Use the PMI to show that 1 2 + 2 2 + . . . + n 2 = n ( n + 1)(2 n + 1) 6 for each natural number n . 5. Let a 1 = 2 a 2 = 4 a n +2 = 5 a n +1-6 a n for all n > 1 . Show that a n = 2 n for all natural numbers n . 2...
View Full Document

This note was uploaded on 12/13/2011 for the course MATH 300 taught by Professor Staff during the Fall '11 term at South Carolina.

Page1 / 2

99Se2 - 1 1a Prove Theorem 2.7g namely Let A and B be sets...

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

View Full Document
Ask a homework question - tutors are online