Construct a flowchart proof to prove the following. Given: 6(x - 3) ≤ 4x - 2 - 6x Prove: x ≤ 2

Q: 2. Show that for any real number c, there is exactly one integer in the interval (c,c + 1].

A: As per guidelines, I can do only first question.

Q: 1. Create a flow proof of the following result: For every real number x, if (x − 3)² ≤ 0, then 10-…

A:

Q: Find the smallest positive integer in the given set. (a) {6u + 15v : u, v ∈Z}    (b) {12r + 17s : r,…

A: Given: (a) { 6u+15v:u,v∈Z }(b) { 12r+17s:r,s∈Z }

Q: Pex)=\X+14 aud hex)= x-1 state functions. following domains, of the following 4sing interval…

A:

Q: b) Prove that |x| ≤ 1 implies that |x² + 2x - 3| ≤ 4|x − 1].

A:

Q: How would you use the existence and uniqueness theorem here?

A: Here the given initial value problem is,.Existence and Uniqueness theorem :The solution of an…

Q: 3. Show that all integers n ≥ 2 can be expressed as 2x + 3y for some nonnegative integers r and y.

A: Mathematical induction is a proof technique used in mathematics to establish the truth of a…

Q: Give a direct proof of the following statement. If x is an even integer, then x² – 6x + 5 is odd. |

A: Remark: We know that addition or subtraction of an even and an odd integer is always an odd integer.…

Q: Suppose that x is a real number and that UCR. Prove that the following two conditions are…

A:

Q: Exercise 9.3.9. To test whether the number n is a prime, you divide n all the integers 1, 2, 3,...…

A:

Q: Show that ACB implies |A|≤|B|.

A:

Q: Which of the following defines the domain of |4x-8<12? A) -8<x<-4 B)-4 <x < 8 C) -1<x< 5 D) 1<x<5

A: We can solve the inequality in order to get the solution.

Q: Proof the following statement in detail: ". Let x ∈ R. Prove that if 3x4 + 1 ≤ x7 + x3, then x >…

A: