GROUP 88) a) List the elements of each of the following sets, using the .' notationwhere necessary:i) {x:x is a positive integer and (3x – 1)( x + 2) = 0}ii){x : 2x is a positive integer}iii) Determine the cardinality of the set{: x is an integer and c)Each of the following is the graph of a function A → B (where Aand B are subsets of R). Determine whether or not each function is:(a) injective; (b) surjective.(i)d)Let S denote the set of four – digit numbers made from the digits 0, 2, 3, 5 and6, where the first digit cannot be 0.i)How many of those in question 8 d) ii) are even?ii)How many of those in question 8 d) ii) are greater than 4,000?

Since it is multiple questions with multipart. As per our company guidelines, we have to solve the…

8) a) List the elements of each of the following sets, using the .' notation where necessary: i) (x:x is a positive integer and (3x – 1)( x + 2) = 0} ii)(x : 2x is a positive integer) iii) Determine the cardinality of the set {:x is an integer andx<%3

8) a) List the elements of each of the following sets, using the .' notation where necessary: i) (x:x is a positive integer and (3x – 1)( x + 2) = 0} ii)(x : 2x is a positive integer) iii) Determine the cardinality of the set {:x is an integer andx<%3

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

GROUP 8
8) a) List the elements of each of the following sets, using the .' notation
where necessary:
i) {x:x is a positive integer and (3x – 1)( x + 2) = 0}
ii){x : 2x is a positive integer}
iii) Determine the cardinality of the set
{: x is an integer and <x <17%}
b) For each of the following relations R on a set A, draw:
List all the ordered pairs, its directed graph, and its binary matrix.
(i)
A = {1, 2, 3, 4, 5, 6, 7, 8}; a Rb if and only if a < b.
(ii)
A = {1, 2, 3, 4, 5, 6, 7, 8}; a R b if and only if a = b.
(iii)
A = {1, 2, 3, 4, 5, 6, 7, 8}; a Rb if and only ifa sb.
(iv)
A = {1, 2, 3, 4, 5, 6, 7, 8}; a R b if and only if" e z.

c)
Each of the following is the graph of a function A → B (where A
and B are subsets of R). Determine whether or not each function is:
(a) injective; (b) surjective.
(i)
d)
Let S denote the set of four – digit numbers made from the digits 0, 2, 3, 5 and
6, where the first digit cannot be 0.
i)
How many of those in question 8 d) ii) are even?
ii)
How many of those in question 8 d) ii) are greater than 4,000?

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