For each integer n, let Tn = {n, n2}. How many elements are in each of T2, T−3, T1 and T0? Justify your answers

Q: Given that So(x) = 1 – for 0 <x< 100, 100 find P(K30 = 25).

A: Given  S0x=1-x100  for  0≤x≤100

Q: 3. In each set of numbers, determine which value(s) are irrational numbers. . 2등, 유, , V9, V8 3 11…

A: The objective of the question is determine the irrational numbers in the given sets.

Q: * For each integer n, let Cn = {n²,n³, nª}. How many elements are in each of C-2, C-1, Co, and C3?…

A: The set always contains the distinct elements. Given Cn = n2 , n3 , n4 Consider C-2 = (-2)2 , (-2)3…

Q: Compute the following: (a) 4!, (b) (), (c) (₂), (d) (), (e) (7), (f) (2)-(2) where n is a…

A:

Q: B. Find e in the whole number. 1. N = 5,000 2. N = 20,000 3. N = 12,000 and n = 200 and n = 3,000 e…

A: B. Here we have to find e in whole number. Formula to calculate e is as,…

Q: Find the value of x if O 1.84 O 1.77 O 1.32 O None of these O 1.52 metazaf =7

A:

Q: Each letter of the alphabet is assigned an​ integer, starting with A=​0, B​=1, and so on. The…

A: Solution: The objective is to find what​ two-letter word is represented by the digits ​02.

Q: For each n e N, let A, = (}, } + ) %3D Find Unen An. Find Nnen An.

A:

Q: For non-negative integer n and r, where 1<rsn, show that (n-r+1)"C,=n(""C,1). r-1

A:

Q: Which of the following is the smallest, positive value of n for which i⁵·iⁿ is equal to - i? *

A: We can use the concept of complex analysis.

Q: The order of the element 3 in Z24 is

A: Given: Z24 Formula Used: The order of an element k in Zn is given by Ok=nhcfk,n

Q: in class of N students where girls and boys and boys ratio is p:q savita ranked rth from the top. if…

A: Total number of students in class= N Ratio of girls to boys: p:q And it is given that Savita ranked…

Q: given the following: A = {x ∈N : x2 ≤ 50}, B = {x ∈Z : −7 3 ≤ x < 4}, C = {x ∈R : |x| < 2} and D =…

A: Note: There are many subparts in the above question. So I will give the answer of the first four…

Q: how many different bases can R^2 and R^3 have?

A: Explain about the count of number of bases of ℝ2 and ℝ3.

Q: For each integer n, let T, = {n, nº}. How many elements are in each of T2, T–3, Tị, and To? Justify…

A: To find:The elements in T2, T-3, T1 and T0.

Q: Solve, if possible, for n where n is an integer in each of the following. b. n³ = a. 2 = -8 c. 2"-27…

A: Given:a. 2n=-8b. n3=-18c 2n.27=1024d  2n.27=16e 3+n2=32+n2f 5n=1257

Q: Find the largest number d such that if |x – 3| < 8, then |5x – 15| < ɛ, where ɛ = 1 Repeat and…

A:

Q: for all integers n >1 E, i = n(n+1} %3D 2

A: To prove the sum of n natural numbers n≥1 is  ∑i=1ni=n(n+1)2

Q: If n E N and n < 2000, how many numbers n have the property that the sum of the digits of n and the…

A: Here n  N and n&lt; 2000. So, n= 1,2,3,........,1999.

Q: For all n, d e Z where d + 0, d\n * n= dk for some kEZ. Disprove: For all integers a, b, and c, if…

A: To disprove that for all integers a, b and c, if a|b+c, the a|b or a|c Suppose a,b,c∈ℤ be any…

Q: Remind yourself what () means. For this class, we will use the convention that () = 0 if n < k or if…

A:

Q: that Edn H(n/d)7(d) = 1 and Edn H(n/d)o(d) = n for all n, where r(n) = d(n) and σ(n) = σι (n) Σm d.…

A:

Q: For all n, d EZ where d + 0, d\n n = dk for some kEZ. Disprove: For all integers a, 6, and c, if…

A: I have disproved the result

Q: Perform the indicated operations: 2n2 + 10n n² +10n + 24 n+4 8n2 + 12n n-1 n² + 8n – 9

A:

Q: (e) Show that every n ≥ 8 can be written as 3a+5b for some a, b € N.

A: Part e asked and answered.

Q: 1. For each pair of integers a and b, find d = gcd(a, b) and find x and y su (a) a = 356, b = 48 (b)…

A:

Q: Which of the following is the smallest, positive value of n for which -i" is equal to -i? (1) n=1…

A:

Q: For each natural number n A, = (-→ 3+n U-1 Find UneN An and NnEN An

A:

Q: If there are 144 A's and 384 B's in 1024 observations. How many (i) AB's and (ii) aß's will there be…

A:

Q: For each of the values on n and d given, find integers q and r such that n = dq + r and 0 is less…

A:

Q: Prove each statement using mathematical inductio n(n+1) 2 1. For all n e Z, E(2i-1)=n? 2. For all n…

A:

Q: If o? = 625, X = 66.3, and Zo.025 = 1.96, %3D %3D %3D then the size n is O 10. None of all. 20. O…

A: None of all

Q: Assume that n(U)=90n(U)=90, n(A)=41n(A)=41, n(B′)=50n(B′)=50, and n(A∪B)=63n(A∪B)=63. Find n(A∩B)

A:

Q: Let R = Z10 O Z100- (a) How many units does R have? (b) How many zero divisors does R have?

A:

Q: For each integer n > 2, let P(n) bè thế för n-1 Eili +2) = n(n-1)(2n + 5) 6. %3D i=1

A: Given                   P(n):   ∑i=1n-1i(i+2)=nn-12n+56,          n≥2

Q: if m is odd and n is odd, demonstrate that m*n=odd

A:

Q: Find the total number of in H.C.F. of n and 36 is 1.

A:

Q: If n E N and n< 2000, how many numbers n have the property that the sum of the digits of n and the…

A: Given that, If n∈ℕ and n&lt;2000 then calculate how many numbers n have the property that the sum of…

Q: Find integers s and t so that s· 201 + t · 302 = 1 . S %3D

A:

Q: Find (r In r)9) and ()").

A: Use the following differntiation formulae, to obtain the required derivatives.…

Q: For each integer n, let Tn = {n, n2}. How many elements are in each of T2, T3,and T1? Justify your…

A: Given that, Tn=n,n2. Substitute n=2 in Tn=n,n2  to find the number of elements in T2. T2=2,22=2,4…

Q: Evaluate the following formula for p1−p2=​0, p=0.140000​, q=1−p​, x1=69​, x2=15​, n1=316​, n2=284​,…

A: Given P-bar=0.140000 n1=316 n2=284

Q: Suppose n (a)= 7a + 4, determine a such that n (a) = 39. %3D

A: GIVEN n(a) = 7a+4 and n(a) = 39

Q: The number ofunits in Z23 [x] is O 22 O 28 None O30

A: Consider the given information: To find the number of units in ℤ23x.

Q: For a populationN = 22,000 and p = 0.14 . Find the for hat p =0.32 for n = 50

A: The value of p hat is 0.32, the sample size n is 50 and the value of p is 0.14.

Q: Find all m, n E N such that: n! + 2n + 49 = m²

A: This problem can be solved by graphical approach. Use a graphing utility to plot the graph of…

Q: For each integer n, let Tn = {n,n²}. How many elements are in each of T2, T–3,T1 and To? %3D Select…

A: Given that for n∈ℕ, Tn=n,n2. Thus number of element in,  1.  T2=2,22T2=2,4 2. T-3=-3,-32T-3=-3,9

Q: For each of the following pairs of numbers (a, b), find ged(a, b) and find integers s and t such…

A: Part a )- Given : Given pairs of the Numbers are 25,30 Calculation: First we find gcd25,30 Therefore…

Q: If n= 2k for some odd integer k, then o(n)= O a. o(k) b. 30(k) O c. 2k d. 20(k) e. None

A:

Q: Find two natural numbers n and m with n, m>26 and gcd⁡(n,m)=26. Then, for the numbers n and m you…

A:

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.