Exercise
Use this result to write an expression for the total number of elements in the power set
Use the binomial theorem as stated in Exercise 25 to evaluate the expression in part a and compare this result to exercise 27 and 37. (Hint: set
If
If
If
Let
Where the binomial coefficients
With
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Elements Of Modern Algebra
- 49. a. The binomial coefficients are defined in Exercise of Section. Use induction on to prove that if is a prime integer, then is a factor of for . (From Exercise of Section, it is known that is an integer.) b. Use induction on to prove that if is a prime integer, then is a factor of .arrow_forwardUse generalized induction and Exercise 43 to prove that n22n for all integers n5. (In connection with this result, see the discussion of counterexamples in the Appendix.) 1+2n2n for all integers n3arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage