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1. For a function f : Z → Z, let R be the relation on Z given by xRy iff f(x) = f(y).
(a) Prove that R is an equivalence relation on Z.
(b) If for every x ? Z, the equivalence class of x, [x], contains exactly one element, what can be said about the function f?
Consider the following linear equations. x1-3x2+x3+x4-x5=8 -2x1+6x2+x3-2x4-4x5=-1 3x1-9x2+8x3+4x4-13x5=49
Submit solutions for all of the following questions. Remember to set out your answers showing all steps completely and explicitly justify your steps. 1. Provide, in no more than
A pair of mittens has been discounted 12.5%. The original price of the mittens was $10. What is the new price? Find 12.5% of $10 and subtract it from $10. Find out 12.5% of $10
Describe what is meant by each of the following NVH terms and explain their importance in vehicle refinement: (a) Vibration absorber (b) Fast Fourier Transform (c) Whit
together, pearl and harvey are going to visit their aunt on sunday. If Pearl visits their aunt every 6 days, while harvey every 8 days, on what day will they visit their aunt toget
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seven more than a number is less than or equal to -18
A telephone company charges $.35 for the first minute of a phone call and $.15 for each additional minute of the call. Which of the subsequent represents the cost y of a phone call
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Type I and type II errors When testing hypothesis (H 0 ) and deciding to either reject or accept a null hypothesis, there are four possible happenings. a) Acceptance of a t
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