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- Show 2 implied 35. Suppose x is transcendental. Show that if k is a positive integer, then ** is transcendental. (Hint: Suppose x is algebraic and write an equation for xk. Show how this gives an equation for a.)5. (1) Show that the lexicographical order on {0, 1} × N with the standard orders on {0, 1} and on N is a well order. (2) Let w be the ordinal of N with the standard order (called the first limit ordinal). The example above has ordinal w+w by the definition of the sum of ordinals. Show that w=w+w.
- Consider the given predicate functions. P(n): "n is a prime number" E(n): "n is an even number" P and E both have domain = {nZ:n>1} Identify the TRUE statement(s). Explain your answer. I. En(E(n)^P(n)) II. Vn(E(n)VP(n)) III. \n(→E(n)→ P(n)) IV. En(-P(n)→→E(n)) O II only O I only O I and II only O II and III only O III only O I and IV only SO IV only O nonenot use ai pleaseTrue or False
- Let f {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} → {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be defined by f(x) = 2x if x 6. Select all the elements of f({5,6}). 01 3 2 4 Select all the elements of f-¹({5,6}). 3 04 Select all the elements of ƒ−¹(ƒ({5,6})). 3 04 2 Select all the elements of ƒ(ƒ¯¹({5,6})). 01 3 04 5 5 06 6 07 07 07 07 U O 8 8 8 8 9 9 9 ✔10 10 10 102.21. Consider the sentence "For every integer n > 0 there is some real number x>0 such that x 0 there is some real number x > 0 such that x < 1/n". Which sentence is true?*39. If x12.27are Which 4-tuples are int the relation {(a, b, c, d) a, b, c, d 0The domain and the rang of the function In (x - 2) are * All x/Zero and y greater than or equal to zero and less than one O All x greater than one and All y All x/zero and All y/Zero O All x greater two and All y x greater than or equal to zero and y greater than or equal to zero and less than one All x and All y/Zero All x/zero and All yRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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