Let a, b, c E Z. Suppose albc and gcd(a, b) = 1. Prove that a|c.

Q: Compute the following. 4! 6! ]*

A: Answer - First we need to understand what is factorial before solving this question  n!…

Q: Let X - N(2, 4). Calculate P[X2 – 4X < 4].

A: P(X2-4X≤4)=0.7602

Q: = Let a, b, and d be positive integers. Prove that if (a, b) : divides a, then (d, b) = 1.

A: Definition of gcd (a, b) =1 is a and b does not have common prime divisor. Using this we can easily…

Q: Is Statement (1) below True or False and WHY? TEA=B is equivalent to "TEA IFF TE B"

A: Let us provide justification and check whether both equations are equivalent or not

Q: Let A = {x € Rx > 5 and x 15 and x 8 and x < 12

A: Given:- A=x∈R|x≥5 and x&lt;18 B=x∈R|x≥15 and x≤22 C=x∈R|x&gt;8 and x&lt;12

Q: what is M<E

A: Solution-As the solution is given,

Q: 5. Prove the following identity for n 2 1: Fzn+1 = F+1+ F;

A: We need to prove that ,  F2n + 1 = F2n+1 + F2n We know that ,   Fm+n = FmFn+1 + Fm-1Fn ,  m ≥ 1 , n…

Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

A:

Q: When is S \ T = T \ S for sets S, T? Give an example

A:

Q: Page 164, 3.1.15* Let X have the pmf p(x) = (1/5)( 4/5)*, x = 0, 1, 2, 3, . . ., zero elsewhere.…

A: Conditional probability : P(A|B) = P(A ∩ B) / P(B)

Q: Let X~Bin(6,0.5), then P(x >4|X >3) is O a. 0.759 O b. 0.524 O C. 0.318 O d. 0.344 O e. 0.143

A: Binomial distribution N=6 P=0.5 q=0.5

Q: Is 1z = 1 for all z ∈ C?

A:

Q: If a € R such that 0 0, then show that a = 0.

A: