Use Contrapositive method to proof the following statement. (a) Suppose a E Z, if a? + 5a is even, then a is even. (b) Suppose y E Z, if y² + 5 is even, then y is odd. (c) Suppose x E Z, if x5 + 7x5 + 5x > x* + x? + 8, then x 2 0.

Q: Letting aa and bb be two positive real numbes such that ab=lab=1, which of the followings is true?…

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Q: In(x²) = 2 ln(x) for all x True O False

A: ln(x^2) =2ln(x) for all x

Q: 1 which of the following is equivalent to 2x-4 O B. -4x²+6x + 5 0 4x²-6x-5 >0 E. 4-2x

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Q: o use divisibility in this problem but i am not sure where to start. Prove or disprove (with a…

A: Introduction: If a and b are integers, a divides b if c is an integer and ac = b. The symbol a|b…

Q: Find the value of |(-1)*+1 – (-1)*+2|. A. -2 B. (-1)" C. 2 D. I(-1)"| E. None of the above.

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Q: Q1 (b): If Xi= 1,3,5,7,9,11 and Yi= 0,2,4,6,8,10. The values of the :following term is i=n 2n – 3…

A: Given,∑i=1i=n2n-3πyi-11+xii-1here n=6

Q: a. 3.2F> Fn+1 for n23 [Solutions and final ans

A: We need to prove 2Fn>Fn+1 Now, we have formula for fibonacci sequence is Fn=Fn-1+Fn-2

Q: dx. Evaluate - 1)²(x² + 2) x+3

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Q: why

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Q: given 7(x-1)=2(3x+2) prove x=11

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Q: 5. -7 | = x(3x + 8). 5x + 1 true false O

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Q: 2) + 2 <0 IX + 31 4,

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Q: P show that (α) |=1 = 12/

A: A detailed solution is given below.

Q: * 4. Determine the conditions under which each of the following conditional sen- tences will be a…

A: (a) The conditional statement "If a + 2 = 5, then 8 &lt; 5" will be true when the expression "a + 2"…

Q: *(2 + 16) (a + 8)(x + 4) 16 where z # a + 8 Submit Question

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Q: b.) 3x-2y < 12

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Q: **2.) In the diagram below, ray NK bisects JNL MJNK-(22-2 and MELNK-(3x)". Determine the value of…

A: Given: In the diagram, the ray NK bisects ∠JNL. m∠JNK=2x2-2°. m∠LNK=3x°. Since the ∠JNL is…

Q: Suppose SCR is a set of numbers. (a) Define inf(S) and sup(S). (b) Show that inf(S) = - sup(-S). (c)…

A: Set: A well-defined collection of objects or numbers is called a set. We can write a set in two…

Q: i=n (5 + у;) (х; — 2) Зп + 2 i=1

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Q: If a * b denotes a² – ab + 2, find the value of 2* (3 * 2). What is the value of x if x * 3 = 0? %3D

A: Given a * b = a2 - ab + 2

Q: ) Recall that r > 0 for every positive real number r. Prove that if a and b are positive real…

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Q: (22²)⁰+ (2⁰). (2²)⁰= 2 O True O false

A: Recall:  a0=1

Q: 5. Which of the following is the value of 7-x+3 when x= -20? (1) 7 (2) 9 (3) 10 (4) 16

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Q: Let P(x) denote the statement "x < 4." P(4) is A) True False

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Q: If xER then |1– x| = |x+1|- True O False

A: We have check given statement is true or not

Q: 4. Find the first three terms of (3x – 2)20. What is the coefficient of æ10?

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Q: (a)  Evaluate S(3, 1, −2). (b) Evaluate S(S(3, 1, −2)). (c) Evaluate S(2a, 3a + b, b − 2a), where…

A: S(3,1,-2) A=3-4-21250118 Now, S(v)=Av ⇒S(3,1,-2)=31-23-4-21250118=10-32-17

Q: 8) Find the derivative of each function: 2. a)g(x) = 3x +5x

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Q: Compute x3 in two ways: by computing x, and x₂, and by computing P³ 0.1 0.2 -~8 0.9 0.8 -0₁ ₂2-0…

A: The given matrix is, P=0.10.20.90.8,x0=10. The value x3 was obtained from: Now, x1can be computed…

Q: Evaluate: xP P n-1 n-2° -1

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Statements and Logic

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