Exercise 3. Consider the structure (Z+, *) of the positive integers with multipli- cation. Show that the following sets are definable: {1}. • The set P of all primes. Show that if A is a definable set in this structure then either P C A or ANP= Ø.

Q: rivial of

A: To find the non trivial of Z8 as,

Q: Show that the square of any integer is of the form 3m or 3m+1 but not of form 3m+2.

A: Proof :-

Q: Let a and b be integers, such that: a + 5b and: 5a - b, are both divisible by 2002. Try that; a² is…

A:

Q: find the 2003 quotiont 40+ 3 when divPde polynomial by c+ I

A:

Q: find the generated of zy zs+Z7

A:

Q: Determine whether the statement is true or false. Justify your answer with a proof or…

A: Yes, the product of  even integer and any integer equal to even

Q: 2. Expand by multiplying 'o) a) (3x+ 4)(2x - 2) b) (2x - 7)(-4x + 5) c) -4y(-4x -5y)

A: Given  a) (3x+4)(2x-2) Multiplying,  (3x+4)(2x-2) = (3x)(2x-2)+4(2x-2)…

Q: Identify the end behavior for the following polynomial a) ↑↑ 个个 8r7 +5x³2x² + 1 此 b) ↓ c) ↑↓ d) ↓↑

A: Given function fx=8x7+5x5-2x2+1 Identify the end behaviour of the polynomial.

Q: Find the product AB if

A: Given: A=12-340-2 and B=5-420-16317058

Q: 10. Which of the following polynomials is NOT divisible by (3x+ 1)? A. 6x2 + 17x+ 5 B. 3x - 4x2+…

A: Use remainder theorem

Q: Add the following polynomials. 4x - 5x +4 2 -8x +4x -1 4x -5x +4 .2 + - 8x +4x - 1

A: It just like a simple addition. Just add the constants then the coefficients of x and then the…

Q: 5. What is the end behavior to the left and right of the following polynomials? a) ODD degree with a…

A:

Q: 3) Show that (a + b +c)² = a² + b² + c² + 2ab + 2ac + 2bc is a polynomial identity.

A: To show: a+b+c2=a2+b2+c2+2ab+2ac+2bc

Q: find the product of 4 6/4×3 4/3

A:

Q: Divide the following polynomials k- 4k* - 3k - 5k + 6k – 3

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Choose all the factor pairs of 54 O -3 and -18 2 and 27 6 and -9 7 and 8 -2 and 27 -6 and -9 -1 and…

A:

Q: What is the order of Z11?

A: Recall the fact that order is the number of elements in that group. Note that ,…

Q: Which of the following expressions can be written as (ax+b)(ax-b), where a and b are integers?…

A: To express which of the following expressions can be written as (ax+b)(ax-b), where a and b are…

Q: A local city wants to compare the number of those with a car and those without a car, represented by…

A: Given,          A local city wants to compare the number of those with a car and those without a…

Q: Simplify the following polynomial by combining like terms. 6d - 10 + 3f – 58 – 3d + 4 O -15d + 3d +…

A:

Q: label the  polynominals of X2 - 18x + 32 =0

A:

Q: Show that the polynomial x + x

A:

Q: The product of any integer and 2 is greater than 2.

A:

Q: Use long division to divide the following polynomials: (3ct + a3-#+1) 은 (22-2x + 1) O 3a2-5x +12 +…

A: Answer

Q: 2. Simplify the following polynomials: a) (x²-3x² + 5x-9) + (4x³ - 5x² - 8x +11) b) (3xyz - 4x² + 8)…

A: For solving this kind of problem we need to add same power of terms and simplify the equation.

Q: spt spt +r(1 pt) (Section 1.9) Let Pt+1 model. Let s = 1.3 be the growth rate of species 1 and r =…

A: Let pt+1=f(pt) be a system and p* be an equilibrium,  then If |f'(p*)|<1 , then p* is stable. If…

Q: Add or subtract the following polynomials. (6d – 10d + 3f) - (5d + 3d – 4) O -10d + 3d + 3d + 4 O -…

A:

Q: if two even integers are multiflied, then the product is also even

A: Ans. True

Q: Questlon Multiply. (5+x)(5 - x) = %3D

A:

Q: Find the product. Assume variables represent positive real numbers. 2) 2x2/5(x11/5-3x) A)2x13/5 -…

A:

Q: b. Find a QR-factorisation of 1 -1 1 1 1 1 -1 0 |

A: Step:-1 Given matrix  is  110-1010111-10 Let  A= 110-1010111-10 Now, we'll apply Gram-Schmidt…