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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
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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