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Binomial Coefficients: Selected Exercises

Binomial Coefficients: Selected Exercises. Preliminaries. What is the coefficient of x 2 y in (x + y) 3 ? (x + y) 3 = (x + y)(x + y)(x + y) = (xx + xy + yx + yy)(x + y) = xxx + xyx + yxx + yyx + xxy + xyy + yxy + yyy = x 3 + 3x 2 y + 3xy 2 + y 3 . The answer thus is 3 .

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Relations & Their Properties: Selected Exercises

Relations & Their Properties: Selected Exercises. 10. Which relations in Exercise 4 are irreflexive? A relation is irreflexive ? ? a ? A (a, a) ? R. Ex. 4 relations on the set of all people: a is taller than b . a and b were born on the same day. a has the same first name as b .

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Selected exercises - PowerPoint PPT Presentation

Binomial Coefficients: Selected Exercises

Relations &amp; Their Properties: Selected Exercises

Relations & Their Properties: Selected Exercises