18th Edition

ISBN: 9781323910528

Author: Lial

Publisher: PEARSON C

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

Chapter 1.6, Problem 1E

(a)

To determine

The correct match(s) for the statement,” Identity element for addition” from the given options.

(b)

To determine

The correct match(s) for the statement,” Identity element for multiplication” from the given options.

(c)

To determine

The correct match(s) for the statement,” Additive inverse of a ” from the given options.

(d)

To determine

The correct match(s) for the statement,” Multiplicative inverse, or reciprocal, of the non-zero number a ” from the given options.

(e)

To determine

The correct match(s) for the statement,” The number that is its own additive inverse” from the given options.

(f)

To determine

The correct match(s) for the statement,” The two numbers that are their own multiplicative inverses” from the given options.

(g)

To determine

The correct match(s) for the statement,” The only number that has no multiplicative inverses” from the given options.

(h)

To determine

The correct match(s) for the statement,” An example of the associative property” from the given options.

(i)

To determine

The correct match(s) for the statement,” An example of the commutative property” from the given options.

(j)

To determine

The correct match(s) for the statement,” An example of the distributive property” from the given options.

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Chapter 1.5, Problem 136E

Chapter 1.6, Problem 2E

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Q1lal Let X be an arbitrary infinite set and let r the family of all subsets F of X which do not contain a particular point x, EX and the complements F of all finite subsets F of X show that (X.r) is a topology. bl The nbhd system N(x) at x in a topological space X has the following properties NO- N(x) for any xX N1- If N EN(x) then x€N N2- If NEN(x), NCM then MeN(x) N3- If NEN(x), MEN(x) then NOMEN(x) N4- If N = N(x) then 3M = N(x) such that MCN then MeN(y) for any уем Show that there exist a unique topology τ on X. Q2\a\let (X,r) be the topology space and BST show that ẞ is base for a topology on X iff for any G open set xEG then there exist A Eẞ such that x E ACG. b\Let ẞ is a collection of open sets in X show that is base for a topology on X iff for each xex the collection B, (BEB\xEB) is is a nbhd base at x. - Q31 Choose only two: al Let A be a subspace of a space X show that FCA is closed iff F KOA, K is closed set in X. الرياضيات b\ Let X and Y be two topological space and f:X -…

Q1\ Let X be a topological space and let Int be the interior operation defined on P(X) such that 1₁.Int(X) = X 12. Int (A) CA for each A = P(X) 13. Int (int (A) = Int (A) for each A = P(X) 14. Int (An B) = Int(A) n Int (B) for each A, B = P(X) 15. A is open iff Int (A) = A Show that there exist a unique topology T on X. Q2\ Let X be a topological space and suppose that a nbhd base has been fixed at each x E X and A SCX show that A open iff A contains a basic nbdh of each its point Q3\ Let X be a topological space and and A CX show that A closed set iff every limit point of A is in A. A'S A ACA Q4\ If ẞ is a collection of open sets in X show that ẞ is a base for a topology on X iff for each x E X then ẞx = {BE B|x E B} is a nbhd base at x. Q5\ If A subspace of a topological space X, if x Є A show that V is nbhd of x in A iff V = Un A where U is nbdh of x in X.

+ Theorem: Let be a function from a topological space (X,T) on to a non-empty set y then is a quotient map iff vesy if f(B) is closed in X then & is >Y. ie Bclosed in bp closed in the quotient topology induced by f iff (B) is closed in x- التاريخ Acy الموضوع : Theorem:- IP & and I are topological space and fix sy is continuous او function and either open or closed then the topology Cony is the quatient topology p proof: Theorem: Lety have the quotient topology induced by map f of X onto y. The-x: then an arbirary map g:y 7 is continuous 7. iff gof: x > z is "g of continuous Continuous function f

Chapter 1 Solutions

INTEGRATED REV.F/BEG.+INT.ALG.W/ACC.>C<

Ch. 1.1 - Concept Check Decide whether each statement is...Ch. 1.1 - Concept Check Decide whether each statement is...Ch. 1.1 - Concept Check Decide whether each statement is...Ch. 1.1 - Concept Check Decide whether each statement is...Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Concept Check For each expression, label the order...Ch. 1.1 - Concept Check For each expression, label the order...Ch. 1.1 - Concept Check For each expression, label the order...

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The correct match(s) for the statement,” Identity element for addition” from the given options.

Solution Summary: The author explains that the correct match(s) for the statement, Identity element for addition, is 0.

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The correct match(s) for the statement,” Identity element for addition” from the given options.

The correct match(s) for the statement,” Identity element for multiplication” from the given options.

The correct match(s) for the statement,” Additive inverse of a ” from the given options.

The correct match(s) for the statement,” Multiplicative inverse, or reciprocal, of the non-zero number a ” from the given options.

The correct match(s) for the statement,” The number that is its own additive inverse” from the given options.

The correct match(s) for the statement,” The two numbers that are their own multiplicative inverses” from the given options.

The correct match(s) for the statement,” The only number that has no multiplicative inverses” from the given options.

The correct match(s) for the statement,” An example of the associative property” from the given options.

The correct match(s) for the statement,” An example of the commutative property” from the given options.

The correct match(s) for the statement,” An example of the distributive property” from the given options.

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Chapter 1 Solutions