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is obtained at least twice? (b) How many times must two dice be rolled to guarantee that score is obtained at least twice? (c) How many times must two dice be rolled to guarantee that score is obtained at least three times? A drawer contains a dozen brown socks and a dozen black socks, A man takes socks out at random in the dark. (a) How many socks must he take out to be sure that he has at le the same colour? (b) How many socks must he take out to be sure that he has at socks? Let A = {1, 2, 3} and B = {a, b}. Determine the set A x B. %3D Let A be a set. Determine the set A x 0.

is obtained at least twice? (b) How many times must two dice be rolled to guarantee that score is obtained at least twice? (c) How many times must two dice be rolled to guarantee that score is obtained at least three times? A drawer contains a dozen brown socks and a dozen black socks, A man takes socks out at random in the dark. (a) How many socks must he take out to be sure that he has at le the same colour? (b) How many socks must he take out to be sure that he has at socks? Let A = {1, 2, 3} and B = {a, b}. Determine the set A x B. %3D Let A be a set. Determine the set A x 0.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 33EQ
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= {n e Z | VI.1. Let 25Z be the set of all integers that are multiple of 25, 25Z = 25k, for some integer k}. Prove that 25Z has the same cardinality as the set of even integers. VI.2. Use the pigeonhole principle to give solutions to the following problems: (a) How many times must a single die be rolled to guarantee that some number is obtained at least twice? (b) How many times must two dice be rolled to guarantee that the same total score is obtained at least twice? (c) How many times must two dice be rolled to guarantee that the same total score is obtained at least three times? VI.3. A drawer contains a dozen brown socks and a dozen black socks, all unmatched. A man takes socks out at random in the dark. (a) How many socks must he take out to be sure that he has at least two socks of the same colour? (b) How socks? many socks must he take out to be sure that he has at least two black VI.4. Let A ={1, 2, 3} and B = {a,b}. Determine the set A × B. VI.5. Let A be a set. Determine the set A × Ø.
Transcribed Image Text:= {n e Z | VI.1. Let 25Z be the set of all integers that are multiple of 25, 25Z = 25k, for some integer k}. Prove that 25Z has the same cardinality as the set of even integers. VI.2. Use the pigeonhole principle to give solutions to the following problems: (a) How many times must a single die be rolled to guarantee that some number is obtained at least twice? (b) How many times must two dice be rolled to guarantee that the same total score is obtained at least twice? (c) How many times must two dice be rolled to guarantee that the same total score is obtained at least three times? VI.3. A drawer contains a dozen brown socks and a dozen black socks, all unmatched. A man takes socks out at random in the dark. (a) How many socks must he take out to be sure that he has at least two socks of the same colour? (b) How socks? many socks must he take out to be sure that he has at least two black VI.4. Let A ={1, 2, 3} and B = {a,b}. Determine the set A × B. VI.5. Let A be a set. Determine the set A × Ø.
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