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(a) Write the negation of the following statement without using "negative" words (such as "no", "not", "none", stc). No justification required for this question. "Every student in this class is taking at least five course." (b) Determine which of the following statements is/are equivalent to the following statement. "If a student likes mathematics, then they like proofs."e Choose all that apply. There may be more than one correct answer. No justification required for this question. (i) "If a student likes proofs, then they like mathematics."e (ii) "If a student dislikes proofs, then they dislike mathematics."e (iii) "If a student dislikes mathematics, then they dislike proofs." (iv) "All math students like proofs."e (v) "All students who like proofs like mathematics."e (c) Express the following sets as either an interval, a union of intervals, a finite set, or the empty set. Note: in this course, the natural numbers N start at zero. No justification required for this question. (i) S= {x ER : 3y € [4,00) such that x>y}. (ii) T = { x € R : r³ – a³ < 0}. (iii) U = { x € N : r3 – x <0}. (iv) W = {x € Z : Vn e Z, x = 2n +1},e

(a) Write the negation of the following statement without using "negative" words (such as "no", "not", "none", stc). No justification required for this question. "Every student in this class is taking at least five course." (b) Determine which of the following statements is/are equivalent to the following statement. "If a student likes mathematics, then they like proofs."e Choose all that apply. There may be more than one correct answer. No justification required for this question. (i) "If a student likes proofs, then they like mathematics."e (ii) "If a student dislikes proofs, then they dislike mathematics."e (iii) "If a student dislikes mathematics, then they dislike proofs." (iv) "All math students like proofs."e (v) "All students who like proofs like mathematics."e (c) Express the following sets as either an interval, a union of intervals, a finite set, or the empty set. Note: in this course, the natural numbers N start at zero. No justification required for this question. (i) S= {x ER : 3y € [4,00) such that x>y}. (ii) T = { x € R : r³ – a³ < 0}. (iii) U = { x € N : r3 – x <0}. (iv) W = {x € Z : Vn e Z, x = 2n +1},e

Advanced Engineering Mathematics
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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(a) Write the negation of the following statement without using "negative" words (such as "no", "not", "none", stc). No justification required for this question. "Every student in this class is taking at least five course." (b) Determine which of the following statements is/are equivalent to the following statement. "If a student likes mathematics, then they like proofs."e Choose all that apply. There may be more than one correct answer. No justification required for this question. (i) "If a student likes proofs, then they like mathematics."e (ii) "If a student dislikes proofs, then they dislike mathematics."e (iii) "If a student dislikes mathematics, then they dislike proofs." (iv) "All math students like proofs."e (v) "All students who like proofs like mathematics."e (c) Express the following sets as either an interval, a union of intervals, a finite set, or the empty set. Note: in this course, the natural numbers N start at zero. No justification required for this question. (i) S= {x ER : 3y € [4,00) such that x>y}. (ii) T = { x € R : r³ – a³ < 0}. (iii) U = { x € N : r3 – x <0}. (iv) W = {x € Z : Vn e Z, x = 2n +1},e
Transcribed Image Text:(a) Write the negation of the following statement without using "negative" words (such as "no", "not", "none", stc). No justification required for this question. "Every student in this class is taking at least five course." (b) Determine which of the following statements is/are equivalent to the following statement. "If a student likes mathematics, then they like proofs."e Choose all that apply. There may be more than one correct answer. No justification required for this question. (i) "If a student likes proofs, then they like mathematics."e (ii) "If a student dislikes proofs, then they dislike mathematics."e (iii) "If a student dislikes mathematics, then they dislike proofs." (iv) "All math students like proofs."e (v) "All students who like proofs like mathematics."e (c) Express the following sets as either an interval, a union of intervals, a finite set, or the empty set. Note: in this course, the natural numbers N start at zero. No justification required for this question. (i) S= {x ER : 3y € [4,00) such that x>y}. (ii) T = { x € R : r³ – a³ < 0}. (iii) U = { x € N : r3 – x <0}. (iv) W = {x € Z : Vn e Z, x = 2n +1},e
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