P3.6.8 Problem: Consider the set S = ZV2] as defined in Exercise 3.6.6, a set of real numbers. (Exercise 3.6.6 says "Let r be any integer. If r is positive, Vr is a real number, and if r is negative, Vr is an imaginary number. In either case, we can consider the set Z[/r]) of the numbers that can be written as a + byr for integers a and b." ) (a) Recall that a unit is an element with norm 1 - what are the units in S? (b) Prove that 7 is not prime in S (c) (harder) Prove that 5 is prime in S

Q: For any real number a, a ≠ 0, show that a+4 a+7 a+5 a +8 = 0, a+6 а+9 a+1 a+2 a+3 and 4a7a 5a 8a =…

A: We are required to prove: a+1a+4a+7a+2a+5a+8a+3a+6a+9=0a4a7a2a5a8a3a6a9a=0aa4a7a2a5a8a3a6a9=0

Q: Let 4; = {0, i} . Find U4, and N 4. i= 1 | A;. i= 1

A: Given :  Ai =  0 , i    To find :  The union ∪i=1∞ Ai    and the intersection  ∩i=1∞ Ai   .

Q: 1. Let P(A) = 0.3 and P(B) = 0.6. a) Find P(AUB) when A and B are independent. b) Find P(A/B) when A…

A: P(A) = 0.3P(B) = 0.6

Q: 5. Use set builder notation to specify the following sets: * (a) The set of all integers greater…

A:

Q: fond the dertive YfY-V5R-47

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Q: 2 -1 Let A = Show that the equation -6 3 b2 Ax = b does not have a solution for all possible b, and…

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Q: Prove that A2=I.

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Q: Determine the slope of the line through the points (-1, 8) and (-1, -4). Plot the points on the…

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Q: . If n(A) = 30, n(B) = 40, and n(A ∪ B) = 45,find n(A ∩ B).

A:

Q: List the elements of U(18).

A: The elements in  which are relatively prime to are the elements of ..Two integers  and  are called…

Q: 2.2.12 Prove that if x and y positive real numbers, then Vx+y # Vx+ Vy. Argue by contradiction. are

A: Let x and y are positive real numbers. Also let x+y=x+y Now squaring on both side,we get…

Q: 7. Establish for A is m × n and B, C are n x p, that A(B+C) = AB + AC

A:

Q: 4. Write the following statement symbolically and then prove it: For all real mimbers a and b, if 0…

A: Here given statement, "for all real numbers a, b with 0≤a<b then a2<b2." Symbolically, it can…

Q: 2.3.12 Which of the following statements are true? Explain. (a) 3 a married person x such that V…

A: 2.3.12 a) is False Since, the statements says that there exist a married person x such that for…

Q: 6.2.2 Show that if there are 30 students in the class, and at least 2 have a last name that begin…

A: Consider the provided statement that there are 30 students in a class then at least two have last…

Q: if n(A U B) = 97 and n(A) = n(B) = 69, find n( A ∩ B)

A: We are asked to find n(A∩B)