{"id":124356,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/discreet-math-homeworkmad-2104-online-spring-2017-written-assignment-1-this-assignment-covers-material-from-module-1-lesson-1-3"},"modified":"2017-08-16T05:57:54","modified_gmt":"2017-08-16T05:57:54","slug":"discreet-math-homeworkmad-2104-online-spring-2017-written-assignment-1-this-assignment-covers-material-from-module-1-lesson-1-3","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/discreet-math-homeworkmad-2104-online-spring-2017-written-assignment-1-this-assignment-covers-material-from-module-1-lesson-1-3\/","title":{"rendered":"Discreet math homework\/MAD 2104 \u2013 ONLINE \u2013 Spring 2017 Written Assignment 1 This assignment covers material from Module 1 Lesson 1-3"},"content":{"rendered":"
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Discreet math homework\/MAD 2104 \u2013 ONLINE \u2013 Spring 2017 Written Assignment 1 This assignment covers material from Module 1 Lesson 1-3<\/p>\n

1. Let P, Q, and R be three statements. Determine if the following two statements are logically equivalent: P \u2192 (Q\u2227R) and (\u223c Q\u2228\u223c R) \u2192\u223c P You may use the following <\/p>\n

table to organize your solution: [10 points]
P Q R \u223c P \u223c Q \u223c R (Q\u2227R) (\u223c Q\u2228\u223c R) P \u2192 (Q\u2227R) (\u223c Q\u2228\u223c R) \u2192\u223c P T T T T T F T F T T F F F T T F T F F F T F F F
2. Let P,Q,R,S be four mathematical statements. Suppose P is a false and (R \u2192 S) \u2194 (P \u2227Q) is a true statement, \ufb01nd the truth values of R,S. [10 points] (This can be <\/p>\n

done without a truth table.)
3. Consider the following statement and its proof. What\u2019s wrong with this proof?[10 points] \u201cLet x and y be two positive numbers. If x \u2264 y, then \u221ax \u2264\u221ay.\u201d Proof : <\/p>\n

Suppose \u221ax \u2264\u221ay. Taking the square of both sides, we get x \u2264 y which is true. Therefore, \u221ax \u2264\u221ay. 4. Negate the following statements (a) [5 points] The square of every <\/p>\n

real number is non-negative. (b) [5 points] If \u221ax is a rational number, then x is not a prime number. (c) [5 points] The number x is even or the number y is even. (d) <\/p>\n

[5 points] For every prime number p, there exists another prime number q with q > p.
5. Prove the following statements using direct proof.[10 points each] (a) If x is an even integer, then x2 \u22126x + 5 is odd. (Hint: The following is NOT a proof of this <\/p>\n

statement: \u201cLet x = 2, then x2 \u22126x + 5 = 22 \u22122\u00b74 + 5 = 4\u22124 + 5 = 5 is odd.\u201d) (b) Suppose x,y \u2208R. If x > y, then y3 + yx2 > x3 + xy2. (c) If n is an odd integer, then <\/p>\n

n2 \u22121 is a multiple of 8. (d) Suppose that a, b, c are integers. Prove that if a2|b and b3|c, then a6|c. (e) If d is an integer with d > 2, then the equation x2 + 3x + <\/p>\n

d = 0 has no real solution.
1
(f) If two integers have opposite parity, then their product is even. (Use formal de\ufb01nitions of odd and even numbers in your proof!)
2<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Discreet math homework\/MAD 2104 \u2013 ONLINE \u2013 Spring 2017 Written Assignment 1 This assignment covers material from Module 1 Lesson 1-3 1. Let P, Q, and R be three statements. Determine if the following two statements are logically equivalent: P Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-124356","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/124356","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=124356"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/124356\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=124356"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=124356"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=124356"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}