B) 1) Decide whether the following statements are true or false 3x-1a) The function y=- has a horizontal asymptote at y = 3.x+2b) cos x cos 4x-sin.xsin 4.x = cos(-3x)c) 2 sin(5x) cos(5x) = sin(10x)d) cos² (20)-sin² (20)= cos(0)

We have to decide whether the given statements are true or false.

Answered: 3x-1 a) The function y=- has a…

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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4. Write each statement in symbolic form, and use truth tables to determine if they are logically equivalent: (define any variables you use) A: If you study hard and do all homework, then you will pass the class. B: If you study hard and did not pass the class, then you did not do all your homework.
A,B,C
Consider this statement: "If there is life on Mars, then there has to be water on Mars." Assume that this a TRUE statement. Now answer the following. a) Write the above statement as a sufficient condition. b) Write the above statement as a necessary condition. c) Write the contrapositive of this statement. d) Write the above statement as an "only if" statement. e) Is it possible to write the above statement in "if and only if" form? f) If there is water on Mars, does it mean that there exists life on Mars? Explain.
2. Let p, q andr be the following statements: p: You run 10 laps daily. q: You are healthy. r: You take multi-vitamins. Translate the following into logical notation using p, q and r as logical connectives. a) You run 10 laps daily, you take multi-vitamins, and you are healthy. b) Either you are healthy or you do not run 10 laps daily, and you do not take multi-vitamins. c) If you do not run 10 laps daily or do not take multi-vitamins, then you will not be healthy.
Let p denote the statement "Florida borders Alabama", and let q denote thestatement "Florida borders Mississippi". Put the following into symbolic form:(i) Florida borders Alabama or Mississippi.(ii) Florida borders Alabama but not Mississippi.(iii) Florida borders Mississippi but not Alabama.(iv) Florida borders neither Alabama nor Mississippi.
Write the following statement using the words "if ... then." "To graduate this semester, it is sufficient that you have completed 18 credits. " The statement equivalently written using the words "if . then" is which of the following? A. If you have not completed 18 credits, then you graduate this semester B. If you graduate this semester, then you have completed 18 credits. OC. If you do not graduate this semester, then you have completed 18 credits. O D. If you have completed 18 credits, then you graduate this semester.
1. Given the symbols: p, q, and r, draw the truth table for the following expressions: а. (рла) b. -(p a q) v (p v q) c. (q→p) v- (q→ (pvr))
5.) Draw a truth table based on the boolean expression: x = a·b · c (x = a nba c)

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3x-1 a) The function y=- has a horizontal asymptote at y = 3. x+2 b) cos x cos 4x-sin.xsin 4x= cos(-3x) c) 2 sin(5x) cos(5.x) = sin(10x) d) cos² (20)-sin² (20) = cos(0)