A Transition to Advanced Mathematics
A Transition to Advanced Mathematics
8th Edition
ISBN: 9781285463261
Author: Douglas Smith, Maurice Eggen, Richard St. Andre
Publisher: Cengage Learning
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Chapter 4.4, Problem 9E

(a)

To determine

Tofind:The permutation of the set C={1,2,3,4,5,6,7} .

(a)

Expert Solution
Check Mark

Answer to Problem 9E

The required permutation set is {1,2,3,4,5,6,7} .

Explanation of Solution

Given information:

The given set is C={1,2,3,4,5,6,7} .

Consider the given set C={1,2,3,4,5,6,7} .

For the notation Ic , the permutation of the set is remains same.

Hence, the required permutation set is {1,2,3,4,5,6,7} .

(b)

To determine

To find: The permutation of the set C={1,2,3,4,5,6,7} .

(b)

Expert Solution
Check Mark

Answer to Problem 9E

The required permutation set is {5,6,2,4,1,7,3} .

Explanation of Solution

Given information:

The given set is C={1,2,3,4,5,6,7} .

Consider the given set C={1,2,3,4,5,6,7} .

The given notation is u={(1,5),(6,7),(4,4),(5,1),(3,2),(2,6),(7,3)} .

Here the element x in C is in the place y , if (y,x)u .

Hence, the required permutation set is {5,6,2,4,1,7,3} .

(c)

To determine

To find: The permutation of the set C={1,2,3,4,5,6,7} .

(c)

Expert Solution
Check Mark

Answer to Problem 9E

The required permutation set is {2,5,4,6,1,7,3} .

Explanation of Solution

Given information:

The given set is C={1,2,3,4,5,6,7} .

Consider the given set C={1,2,3,4,5,6,7} .

The given notation is v={(1,2),(2,5),(3,4),(5,1),(4,6),(6,7),(7,3)} .

Here the element x in C is in the place y , if (y,x)v .

Hence, the required permutation set is {2,5,4,6,1,7,3} .

(d)

To determine

To find: The permutation of the set C={1,2,3,4,5,6,7} .

(d)

Expert Solution
Check Mark

Answer to Problem 9E

The required permutation set is {2,1,4,3,5,7,6} .

Explanation of Solution

Given information:

The given set is C={1,2,3,4,5,6,7} .

Consider the given set C={1,2,3,4,5,6,7} .

The given notation is w={(1,2),(2,1),(3,4),(4,3),(5,5),(6,7),(7,6)} .

Here the element x in C is in the place y , if (y,x)w .

Hence, the required permutation set is {2,1,4,3,5,7,6} .

(e)

To determine

To find: The permutation of the set C={1,2,3,4,5,6,7} .

(e)

Expert Solution
Check Mark

Answer to Problem 9E

The required permutation set is {6,1,4,7,5,3,2} .

Explanation of Solution

Given information:

The given set is C={1,2,3,4,5,6,7} .

Consider the given set C={1,2,3,4,5,6,7} .

Now, find uv .

  uv={(1,1),(2,7),(3,5),(4,6),(5,2),(6,3),(7,4)}

Here the element x in C is in the place y , if (y,x)uv .

Hence, the required permutation set is {6,1,4,7,5,3,2} .

(f)

To determine

To find: The permutation of the set C={1,2,3,4,5,6,7} .

(f)

Expert Solution
Check Mark

Answer to Problem 9E

The required permutation set is {1,7,5,6,2,3,4} .

Explanation of Solution

Given information:

The given set is C={1,2,3,4,5,6,7} .

Consider the given set C={1,2,3,4,5,6,7} .

Now, find vu .

  vu={(1,1),(2,7),(3,5),(4,6),(5,2),(6,3),(7,4)}

Here the element x in C is in the place y , if (y,x)vu .

Hence, the required permutation set is {1,7,5,6,2,3,4} .

(g)

To determine

To find: The permutation of the set C={1,2,3,4,5,6,7} .

(g)

Expert Solution
Check Mark

Answer to Problem 9E

The required permutation set is {1,2,3,4,5,6,7} .

Explanation of Solution

Given information:

The given set is C={1,2,3,4,5,6,7} .

Consider the given set C={1,2,3,4,5,6,7} .

Now, find ww .

  ww={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7)}

Here the element x in C is in the place y , if (y,x)ww .

Hence, the required permutation set is {1,2,3,4,5,6,7} .

(h)

To determine

To find: The permutation of the set C={1,2,3,4,5,6,7} .

(h)

Expert Solution
Check Mark

Answer to Problem 9E

The required permutation set is {1,6,7,4,5,2,3} .

Explanation of Solution

Given information:

The given set is C={1,2,3,4,5,6,7} .

Consider the given set C={1,2,3,4,5,6,7} .

Now, find uvw .

  uvw={(1,1),(2,6),(3,7),(4,4),(5,5),(6,2),(7,3)}

Here the element x in C is in the place y , if (y,x)uvw .

Hence, the required permutation set is {1,6,7,4,5,2,3} .

(i)

To determine

To find: The permutation of the set C={1,2,3,4,5,6,7} .

(i)

Expert Solution
Check Mark

Answer to Problem 9E

The required permutation set is {5,3,7,4,1,2,6} .

Explanation of Solution

Given information:

The given set is C={1,2,3,4,5,6,7} .

Consider the given set C={1,2,3,4,5,6,7} .

Now, find u1 .

  u1={(1,5),(2,3),(3,7),(4,4),(5,1),(6,2),(7,6)}

Here the element x in C is in the place y , if (y,x)u1 .

Hence, the required permutation set is {5,3,7,4,1,2,6} .

(j)

To determine

To find: The permutation of the set C={1,2,3,4,5,6,7} .

(j)

Expert Solution
Check Mark

Answer to Problem 9E

The required permutation set is {5,1,7,3,2,4,6} .

Explanation of Solution

Given information:

The given set is C={1,2,3,4,5,6,7} .

Consider the given set C={1,2,3,4,5,6,7} .

Now, find v1 .

  v1={(1,2),(2,1),(3,7),(4,3),(5,2),(6,4),(7,6)}

Here the element x in C is in the place y , if (y,x)v1 .

Hence, the required permutation set is {5,1,7,3,2,4,6} .

(k)

To determine

To find: The permutation of the set C={1,2,3,4,5,6,7} .

(k)

Expert Solution
Check Mark

Answer to Problem 9E

The required permutation set is {2,7,6,3,5,1,4} .

Explanation of Solution

Given information:

The given set is C={1,2,3,4,5,6,7} .

Consider the given set C={1,2,3,4,5,6,7} .

Now, find (uv)1 .

  (uv)1={(1,2),(2,7),(3,6),(4,3),(5,5),(6,1),(7,4)}

Here the element x in C is in the place y , if (y,x)(uv)1 .

Hence, the required permutation set is {2,7,6,3,5,1,4} .

(l)

To determine

To find: The permutation of the set C={1,2,3,4,5,6,7} .

(l)

Expert Solution
Check Mark

Answer to Problem 9E

The required permutation set is {2,7,6,3,5,1,4} .

Explanation of Solution

Given information:

The given set is C={1,2,3,4,5,6,7} .

Consider the given set C={1,2,3,4,5,6,7} .

Now, find v1u1 .

  v1u1={(1,2),(2,7),(3,6),(4,3),(5,5),(6,1),(7,4)}

Here the element x in C is in the place y , if (y,x)v1u1 .

Hence, the required permutation set is {2,7,6,3,5,1,4} .

(m)

To determine

To find: The permutation of the set C={1,2,3,4,5,6,7} .

(m)

Expert Solution
Check Mark

Answer to Problem 9E

The required permutation set is {1,5,6,7,3,4,2} .

Explanation of Solution

Given information:

The given set is C={1,2,3,4,5,6,7} .

Consider the given set C={1,2,3,4,5,6,7} .

Now, find u1v1 .

  u1v1={(1,2),(2,5),(3,6),(4,7),(5,3),(6,4),(7,2)}

Here the element x in C is in the place y , if (y,x)u1v1 .

Hence, the required permutation set is {1,5,6,7,3,4,2} .

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Chapter 4 Solutions

A Transition to Advanced Mathematics

Ch. 4.1 - If possible, give an example of a set A such that...Ch. 4.1 - Let A. Prove that if sup(A) exists, then...Ch. 4.1 - Let A and B be subsets of . Prove that if sup(A)...Ch. 4.1 - (a)Give an example of sets A and B of real numbers...Ch. 4.1 - (a)Give an example of sets A and B of real numbers...Ch. 4.1 - An alternate version of the Archimedean Principle...Ch. 4.1 - Prob. 17ECh. 4.1 - Prove that an ordered field F is complete iff...Ch. 4.1 - Prove that every irrational number is "missing"...Ch. 4.2 - Let A and B be compact subsets of . Use the...Ch. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Assign a grade of A (correct), C (partially...Ch. 4.2 - For real numbers x,1,2,...n, describe i=1nN(x,i)....Ch. 4.2 - State the definition of continuity of the function...Ch. 4.2 - Find the set of interior point for each of these...Ch. 4.2 - Suppose that x is an interior point of a set A....Ch. 4.2 - Let AB. Prove that if sup(A) and sup(B) both...Ch. 4.2 - Let Abe a nonempty collection of closed subsets of...Ch. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prove Lemma 7.2.4.Ch. 4.2 - Which of the following subsets of are compact? ...Ch. 4.2 - Give an example of a bounded subset of and a...Ch. 4.3 - Let A and F be sets of real numbers, and let F be...Ch. 4.3 - In the proof of Theorem 7.3.1 that =, it is...Ch. 4.3 - Assign a grade of A (correct), C (partially...Ch. 4.3 - Prove that 7 is an accumulation point for [3,7). 5...Ch. 4.3 - Find an example of an infinite subset of that has...Ch. 4.3 - Find the derived set of each of the following...Ch. 4.3 - Let S=(0,1]. Find S(Sc).Ch. 4.3 - Prob. 8ECh. 4.3 - (a)Prove that if AB, then AB. (b)Is the converse...Ch. 4.3 - Show by example that the intersection of...Ch. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Let a, b. Prove that every closed interval [a,b]...Ch. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.4 - Prob. 1ECh. 4.4 - Prove that if x is an interior point of the set A,...Ch. 4.4 - Recall from Exercise 11 of Section 4.6 that the...Ch. 4.4 - A sequence x of real numbers is a Cauchy* sequence...Ch. 4.4 - Prob. 5ECh. 4.4 - Assign a grade of A (correct), C (partially...Ch. 4.4 - Prob. 7ECh. 4.4 - Give an example of a bounded sequence that is not...Ch. 4.4 - Prob. 9ECh. 4.4 - Let A and B be subsets of . Prove that (AB)=AB....Ch. 4.5 - For the sequence y defined in the proof of Theorem...Ch. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Let I be a sequence of intervals. Then for each...Ch. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Find all divisors of zero in 14. 15. 10. 101.Ch. 4.5 - Prob. 8ECh. 4.5 - Suppose m and m2. Prove that 1 and m1 are distinct...Ch. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Determine whether each sequence is monotone. For...Ch. 4.5 - Prob. 13ECh. 4.5 - Complete the proof that xn=(1+1n)n is increasing...Ch. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.6 - Prob. 1ECh. 4.6 - Repeat Exercise 2 with the operation * given by...Ch. 4.6 - Prob. 3ECh. 4.6 - Let m,n and M=A:A is an mn matrix with real number...Ch. 4.6 - Let be an associative operation on nonempty set A...Ch. 4.6 - Let be an associative operation on nonempty set A...Ch. 4.6 - Suppose that (A,*) is an algebraic system and * is...Ch. 4.6 - Let (A,o) be an algebra structure. An element lA...Ch. 4.6 - Let G be a group. Prove that if a2=e for all aG,...Ch. 4.6 - Prob. 10ECh. 4.6 - Complete the proof of Theorem 6.1.4. First, show...Ch. 4.6 - Prob. 12ECh. 4.6 - Prob. 13ECh. 4.7 - Give an example of an algebraic structure of order...Ch. 4.7 - Let G be a group. Prove that G is abelian if and...Ch. 4.7 - Prob. 3ECh. 4.7 - (a)In the group G of Exercise 2, find x such that...Ch. 4.7 - Show that (,), with operation # defined by...Ch. 4.7 - Let m be a prime natural number and a(Um,). Prove...Ch. 4.7 - Prob. 7ECh. 4.7 - Prob. 8ECh. 4.7 - Prob. 9E
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