Prove that if n divides a, b, and c, then n³ divides a²(b – c) + b² (a – c) +²(b – a).

Q: If P(A)=0.2, P(B)=0.3, and P(A∪B)=0.5, then P(A∩B)=?

A: Solution

Q: A positive integer N is said to be a congruent number if it is the area of a right triangle with…

A: Given : A Positive Integer Is Said To Be Congruent, If It Is The Area Of A Right Triangle With Sides…

Q: P(A) = 0.8; P(B) = 0.7 and P(A∩∩B) = 0.6.  Determine P(A∪B).

A: Given problem Given that   P( A ) = 0.8 P( B ) = 0.7 P( A ∩ B ) = 0.6  P( A ∪ B ) = ?

Q: Let the size of A be 4×3, B be 3×5, and C be 4×5. Determine whether the following are defined: [3]…

A: Step 1: Given,Matrix A has dimensions 4 × 3Matrix B has dimensions 3 × 5Matrix C has dimensions 4 ×…

Q: Kailashben

A: The objective of this question is to find another permuted LU factorization of the given matrix A.…

Q: Why does the fact that the orders of the elements of A4 are 1, 2, and3 imply that |Z(A4)| = 1?

A: Given: The orders of the elements of A4 are 1, 2, and 3.We need to signify the given fact to imply…

Q: If β is a zero of x2 +x + 2 over Z5, find the other zero.

A: Given: The expression x2+x+2 over  Z5 has β as zero. To find: The other zero of the given…

Q: Show that [o 2] A 3 0 has no A = L-U factorization where L is lower triangular and U is upper…

A:

Q: Given n(U)=70​, n(A)=29​, n(B)=21​, and n(A ∩ B) =4​,  find (A∪B)'

A:

Q: Find Re(2) if z(4 +) -z+ (80 + 96)

A: In the given question we have to find Re(z) if…

Q: Find, if possible, A + B, A- B, 2A, 2A- B, and B + A = 5-6 2 3 -4 1 (a) A + B 183 11 (b) A - B 188…

A:

Q: Assume that n(U)=115n(U)=115, n(B′)=65n(B′)=65, n(A∩B′)=32n(A∩B′)=32, and n(A∩B)=19n(A∩B)=19 Find…

A: Now consider,

Q: Prove that if n is odd, then 2 is not a square in GF(5n) In other words, prove that there is no…

A: PROOF :

Q: Use A−1 to decode the cryptogram.

A:

Q: Let​ n(U) = 40​, ​n(A ∪​ B)′ = 6​, and​ n(A) = 19​, find​ n(B –​ A).   ​n(B –​ A)

A:

Q: Find the values of w, x, y and z in fraction form using (a)Gauss Elimination, (b)Gauss-Jordan…

A: NOTE: According to guideline answer of first question or first method can be given, for other please…

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: LetP(A) = 0.20, P(B) = 0.80, andP(A∩B) = 0.16. Are A and B independent? Justify your result…

A:

Q: What is the remainder of a divided by m if m|a (m divides a)?

A: If b is remainder of that problem then a=mk+b for some integer k

Q: 2. Find the LU factorizations of and 20 5 2 -6 3 -13 -3 4 9 16 17 2 4 -6 2 13 9 دن و ان 5 4

A:

Q: 1) Name the polynomial a) 3x? + 9x - 1 b) 2x* - 9x? - 1

A: a) 3x2+9x-1The above polynomial has a degree 2⇒It is quadratic polynomial

Q: Show that C(2n, n)+C(2n, n−1)= 1/2C(2n+2, n+1).

A: We have to show that: