15. Give examples of the following. Justify your answers.: (b) A set X such that |P(X)| = 8. (c) An integer n such that n is equivalent to 6 (mod 7) and n is equivalent to 0 (mod 5).

Q: Letr be a real number and let k be an integer. We then define the binomial coefficient () by (3)…

A: The Binomial coefficient is defined as: rk=rr-1...r-k+1k! for k≥1  k is an integer and r is a real…

Q: 5. (a) Without evaluating them, determine which of the following are equal, and give reasons: | r|2|…

A:

Q: is less than The following numbers are given in ternary form. Find the real number that each…

A: Introduction: In mathematics, a ternary form is a homogeneous polynomial of degree three in three…

Q: H.W. Evaluate the following expressions for m= 6, n=2, a 0, b 0, c 0, d-0, and e-0 (i) a+=4+ ++m*n ;…

A: Note: According to bartleby we have to answer only first three subparts please upload the question…

Q: (a) 55 mod 7. (b) –101 div 3.

A: (a) 55 mod 7  As 55 = 7•7+6 So that  55 mod 7 = 6 mod 7

Q: The equivalent of Z sub 5 is set of non-negative integers less than 5. What will be the value of 2…

A:

Q: f(x) = e* xo = 0,x1 = 0. 1,x2 = 0.2 %3D %3D

A:

Q: 20. All statements are true EXCEPT: O All non-zero digits are significant. All zeroes between…

A: Significant figures or digits or numbers are basically those numbers that carry some meaningful…

Q: Prove the following statement. You may employ any proof techniques If n € Z, then 4|n² or 4| (n²-1).

A:

Q: .18 Let x, a and 8 be real numbers. Show that the statements |x-al < 8 and a -8 < x < a +8 are…

A:

Q: Find an integer n that would guarantee Simpron's Rule S, to be within 10-8 of ³/2dx. You do not need…

A: Given Information:To find:The integer  for Simpsons' Rule.Concept used:Accracy on Simpson's rule…

Q: Suppose m is a natural number and 2 m and 3|m. Prove that 6|m.

A:

Q: The order of the integer 4 modulo 19 is: O 4 O None of the choices O 6

A: To find The order of the integer 4 modulo 19.

Q: 6.25. every integer n> 4. - 9n - 10) for every nonnegative integer n.l Prove that 1++++ <2- for…

A:

Q: A. Prove the following: 1. For all integers k and 1, if k and 1 are both even, then k+1 is even. 2.…

A:

Q: 8. If a and b are odd integers, then 8|(a² – b²) -

A:

Q: Use a proof by contrapositive to prove that, if (x + 12)/x is an integer, then x < 13.

A:

Q: 7. For all odd integers x and y, x² +3y² = 0 (mod8) . 8. The equation x* +x² +1= 0 has no real…

A:

Q: How many positive integers n less than or equal to 11,347 satisfy d(n) 1 (mod 2)?

A: We need to find a number of positive integers n≤11347 such that d(n)≡1(mod 2) i.e., , k∈Z.So, we…

Q: 9. Prove the following statements. For this question, upload your work as a pdf file (pictures of…

A:

Q: 6. Write down careful proofs of the following statements: (a) √6-√2>1. (b) If n is an integer such…

A: (a) We know,              9 &gt; 8           =&gt; √9 &gt; √8           =&gt; 3 &gt; 2√2…

Q: 3) Two points are plotted on the number line below. 十+ -10 -9 -8 -7-6 -5-4 -3-2-1 十十+ 1 3 10 Which…

A:

Q: Let m be 40 and let n be 9. What are the integers q and r such that m = qn+r and 0 < r < n.?

A:

Q: +1 X What are all of the values of x ,such that (-1) n+ converges? 6 06.2 O 0<x<6.3O x26.4O

A:

Q: Q13/ A/ Find A-B? * 1 11 B= | 2 15 If A = 2 4 -4 find .3 4] 3

A: Here, A=112434,B=0-12-453

Q: VI. Determine four values of x that will satisfy the following. 16. x = 4 mod 5 & x = 3 mod 7

A:

Q: 3. Let S be the congruent modulo 2 relation on Z,that is m S n→ 2|(m-n) . Show the relation

A: A relation is called symmetric if for any  if  then we have .

Q: It is a fact that if n is any nonnegative integer, then 1-(1/2"+1) 1 1 1 1+=+ + + •+ 2 2² 23 1-(1/2)…

A:

Q: Proficiency #7. [Counterexamples] For each of the following two statements, give a counterexample to…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.