hw1f09solns[1] - 1 ISyE 3770 – Fall 2009 Homework #1 —...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 ISyE 3770 – Fall 2009 Homework #1 — Solutions 1. Suppose U = [0 , 2], A = [0 . 5 , 1], and B = [0 . 2 , 1 . 6]. What are A ∪ B , A ∪ B , A ∩ B , and A ∩ B ? Solution: Note that A ⊆ B . Then A ∪ B = [0 , . 2) ∪ (1 . 6 , 2] A ∪ B = [0 , . 2) ∪ [0 . 5 , 1] ∪ (1 . 6 , 2] A ∩ B = [0 , . 5) ∪ (1 , 2] A ∩ B = [0 . 2 , . 5) ∪ (1 , 1 . 6] 2 2. Prove DeMorgan’s Laws. You can use Venn diagrams or argue mathematically. Solution: Let’s prove that A ∪ B = A ∩ B . Proof: x ∈ A ∪ B iff x / ∈ A ∪ B iff x / ∈ A and x / ∈ B iff x ∈ A and x ∈ B iff x ∈ A ∩ B 2 Now let’s prove that A ∩ B = A ∪ B . Proof: x ∈ A ∩ B iff x / ∈ A ∩ B iff x / ∈ A or x / ∈ B iff x ∈ A or x ∈ B iff x ∈ A ∪ B 2 3. A box contains 3 marbles (one red, one green, and one blue). (a) Consider an experiment that consists of taking one marble from the box, then replacing it in the box, and then drawing a second marble from the box. What is the sample space?is the sample space?...
View Full Document

Page1 / 3

hw1f09solns[1] - 1 ISyE 3770 – Fall 2009 Homework #1 —...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online