Find n if: a) P(n, n) = 5040. b) 66= C(n, 2). c) P(n+1, 5)= 5P(n,1) Note: n is a nonnegative integer and parts (a), (b), and (c) are not connected.

Q: In the following, state whether A = B or not:(i) A = { a, b, c, d } B = { d, c, b, a }(ii) A = { 4,…

A:

Q: Let n EU = Z and p(n): n² + n is an even integer. a. Write the following statement: (Vn) p(n). b. Is…

A: (a) Here, the given statement is: For ∀n∈U=ℤ, p(n):n2+n is an even integer.

Q: 4. Write as a single power first, if possible, and then evaluate. a) 5³ x 5 b) 4⁹ ÷ 47 c) (2¹)² -5 •…

A:

Q: Simplify:(3ª)(3a+4)3 A) 34a+4 B) 3a3+ta+12 C) za3+a+144 D) 34a+12

A:

Q: 15. Evaluate L s-3 A) 2e e" +t- 61 +t-61° B) 2e " +1-6t -1– 61 C) 2e" +t-3t² D) 2e" +1-3t

A:

Q: 8:36 6) 343 = k° A. Irwin to you 34s 3 8) 512 = (x + 12)² %3D 10) -5 – 4 - (81n) = -2921 3/2

A:

Q: Any integer of the form 12k + 11 is also of the form а) Зт + 1 b) 5m + 2 4m + 3 бт + 1

A: We have to do proper manipulation.

Q: Q. 02: (a) Verify the commutative propernties of union and Intersection with help of A = (1,2,3,4),…

A:

Q: Q: Let a,,a,, az,--.. be an A.P. with first term a and common difference d. Then, a, =a,a, = a+ d,a,…

A:

Q: mca's a Ik lasb) zd then 巧 is a) Poime c) re latively prime d) of these. none

A: We are given that a,b=d We need to find ad,bd Now, a,b=d means gcda,b=d Now, gcda,b can be written…

Q: 15%0 18.) A two-digit natural number with the same digits is equal to the sum of the positive…

A: The correct option is not available in the question.Since we want a two digit number with same…

Q: "Co 34 "C, "C, "C; (-1)" "C, ,ne Nis equal to 10 14 (4n + 2) 2" n! 2"-n! () 3.5-7...(2n - 1)(2n +1)…

A: We have use binomial theorem  1-xn=nC0 - nC1 x + nC2 x2  + .........+(-1)n   nCn

Q: (22) Prove: Sn: 1 ² + 2 ² + 3² + ... + n² = n(n+₁) (2nti) neN

A:

Q: Any integer of the form 12k +11 is also of the form a) 3m + 1 b) 5m +2 4m + 3 6m + 1

A: Answer

Q: Let p, q, and r be prime natural numbers with p # q and n= p2q. Then, all the subfields of GF(r")…

A: Answer: Option (C) Given that, p,qand r are prime natural numbers and n is positive integer. Let F…

Q: 7) Use a direct proof to show that: a) The sum of an even integer and an odd integer is odd. b) If n…

A: Use the following concepts, to obtain the required result. An even integer m can be written as a…

Q: 3. Prove by contradiction, that if x and y are odd integers, then there is no integers z such that…

A:

Q: 6. Simplify these algebraic expressions. a) 2m + 12n - 3m - Op+ 10p +m – n- 12p b) 5r+ 13t +…

A:

Q: 11! 1.) 5!x4!x3! 2.) Р(8, 5) 3.) Р(12, 4)

A: Our aim is to solve the following :  1) 11!/(5!*4!*3!) 2) 10!/7! 3) P(8,5) As per our guidelines, we…

Q: 3 Suppose that ID cards are made in the shape of an equilateral riangle, with n equidistant lines…

A: n= 6m+5

Q: prone 2 + 4 + 6 + + 2n = n(n+1). for every nz 2.

A:

Q: 23 - where a and b are positive integers; How many b values are there for the condition 2a + 3b =…

A:

Q: $(7n) = (n) if 7 divides n and 7. 70(n) if 7 divides n and 60(n) if 7 does not divide n (n) if 7…

A:

Q: 71 E(k – 1) F18

A: see 2nd step

Q: I need help

A: To find:∫013481-u221+u23du

Q: 4s + 32 L-1 (s² – 16). wwww.

A: Given that  (4s+32)/(s^2-16) To determine the inverse Laplace

Q: Q-3: a) For all integers a, b, c, d, determine whether each of the following is TRUE or FALSE,…

A:

Q: 37! D- Given that N= (191)(15) is an integer: i- Does the prime 11 divide N? What about the prime…

A: N = 37!19! 15!37! consist numbers that are divided by 11→11, 22 , 33→319! consist numbers that are…

Q: How would you respond to Tawana, who claims that mn is the least common multiple of m and n in every…

A: Consider two natural numbers m, n.   Then, the multiples of m are m, 2m, 3m, 4m   and the multiples…

Q: 11) | 8 + 4n| 4 -10 > 3 -8 -6 -4 0 2 12) 1 + −1 + 4m ≥ 32 -8 0 + + 4 8 12

A:

Q: only d)

A:

Q: (m")(2*)(m)(m³) (m')(2) Simplify and then evaluate for m = 3 and n= 7. %3D O a) (m*)(2?) = 3969 %3D…

A:

Q: mwwwppppna tind the Probuce 5) 5122-1)0-22 +32-4)

A: To determine the product of the polynomials.

Q: 4. Find the sum of positive divisor of 5,020 and also find the pair of this number so that they can…

A: We have to find the sum of all divisor of 5020 and then the amicable pair of the number.

Q: If n = 12 m (me N), prove that "C₂ (2+√3)² "Co- - + "C4 (2+√√3)4 n "C6 (2+√3)6 ·+···=(-

A:

Q: O d. 3 34 9x + 3 Which of the following expressions does not represent the sum: Select one: O a. 2k…

A:

Q: -2x 6. A) Find dx 2x 1.

A: We have to find derivative

Q: Which of the answers below is the ordering of these running times from fastest to slowest? a)…

A: We have to arrange the following sequences in order from fastest running times to slowest. (a)…

Q: Which choice gives an example that supports the conjecture, and a counterexample that nows the…

A:

Q: State the excluded values for each. 60x 1) 12x 702 2) 100 n+6n + 5 4) m+7 3) m +4m-21 n+1

A:

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

A: