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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 equivalenc
What is 2 5 ? 2 5 = 2 ×2 ×2 ×2 ×2 = 32
If cos?+sin? = √2 cos?, prove that cos? - sin? = √2 sin ?. Ans: Cos? + Sin? = √2 Cos? ⇒ ( Cos? + Sin?) 2 = 2Cos 2 ? ⇒ Cos 2 ? + Sin 2 ?+2Cos? Sin? = 2Cos 2 ? ⇒
Negative function : Several functions are not positive however. Consider the case of f (x ) =x 2 - 4 on [0,2]. If we utilizes n = 8 and the midpoints for the rectangle height w
Realtors estimate that 23% of homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that at most
Objectives After going through this unit, you should be able to 1. explain the processes involved ih addition and subtraction; 2. plan and execute activities that woul
Array - when items are arranged in a regular rectangular pattern of rows and columns, counting how many there are. (e.g., if there are 3 rows of 5 girls each, how many girls are t
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
Which general famously stated 'I shall return'? A. Bull Halsey B. George Patton C. Douglas MacArthur D. Omar Bradley
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