Show that 5 – V7 is an algebraic number.

Q: _If A = Verify that [A-!]" = [A"]¬1 ? l1 2.

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Q: Prove by cases that 25x² + 35x is an even integer whenever 5x-7 is an integer. Note here that the…

A: Apply the condition for 5x-7 to be an integer case by case.

Q: Show by contraposition that for any real number x if - 5 < x< 4 then x2+x – 20 < 0

A: For the solution follow the next step.

Q: 1. Show that subtraction is not associative for the set of integers.

A: Definition :Let "." be a binary operation and A is a setThen "." is said to be associative for A if…

Q: Use a direct proof to show that if a and b are positive integers, then +> 2. Hint: Rewrite the…

A: We are given that a and b are positive integers, that means, a≥0 and b≥0 Now, the square of any…

Q: Justify that every prime number except 2 and 3 has the form 6q + 1 or 6q + 5 for some integer q.

A: Let p be a prime number other than 2 and 3. If p is divided by 6, then by the quotient-remainder…

Q: TRUE OR FALSE  x and y are POSITIVE integers.

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Q: Show that if a positive integer is odd, then it's square is odd.

A: To show that if a positive integer is odd then its square is odd

Q: Let a and b be integers. Show that if every integer that divides a also divides b, then a | b. (a…

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Q: Show by contraposition that for positive real numbers a and b, if ab - a - b ≥0 then a and b are…

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Q: If x is an odd integer then 5x – 7 is an even integer.

A: 5 and x are odd integers. Multiplication of two odd integers is always odd. Hence, 5x is an odd…

Q: 23. Prove that any integers a,9(a?-3)

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Q: Show that if a1,: a2., an are integers that are not all 0 and c is a positive integers, then…

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Q: Find a number that provides a counterexample to show that a given statement is false, For all number…

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Q: Show by contraposition that for any real number x if -5 <x<4 then x2+x- 20 <0

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Q: Find all integer numbers a for which

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Q: 9. Use fix) = 3-4 and gix)-5-2' to evaluate the expressions in simplitied form: * (g )

A: We have the given functions as f(x)=3x-4g(x)=5-2x3   We have to find (a) f∘g(x) (b) g∘f(x)

Q: Let a be a real number. Prove by contrapositive that if a+ 7x = 90, then a < 4.

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Q: find all possible three-digit numbers that are of the form 75_ and are divisible by both 3 and 2

A: Since the number is divisible by 2 and 3, it must be divisible by 6.

Q: Determine whether the statement is true or false. 1 dr In (8) x2 -

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Q: Find the value of x to make a counterexample to the conjecture. Conjecture: For all numbers x,…

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Q: For any integer a, show that a²-a+7 ends in one of the digits 3, 7, or 9.

A: For any integer a , we have to show that a2 - a + 7 ends in one of the digits 3 , 7 , or 9 . Note…

Q: (c) Show that 3/2+ 2/3 is an algebraic number?

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Q: from the list 0, 14, 2/3 , π, √7, -11/14 , 2.34, -19, 55/8, -√17, 3.2 ̅1, and -2.6, identify each of…

A: Given list of numbers are, 0, 14, 23, π, 7, -1114, 2.34, -19,  558, -17,3.21, -2.6.

Q: Show that for all integers a, b > 0, the number (a + b) – (a O b) is both nonnegative and even.

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Q: for divisibilty by each of

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Q: Use forward reasoning to show that if x is a nonzero real number, then x2 + > 2.

A: The detailed solution is as follows below:

Q: Develop a simple expression for the entries of A", where n is a positive integer and 1 A = -IN -IN

A: To get a simple expression for the entries of An, where n is a positive integer. A=112012

Q: The positive integers that are divisors of 68 are

A: We will use multiple method to find all the divisor of the given number .

Q: 2. Determine all values of x - y when x and y are integers such that x = 360 + y².

A: The given equation is. x2=360+y2x2-y2=360x+yx-y=360 Since it is given that x and y are integers, so…

Q: Show that 3-4" + 51 is divisible by 3 and 9 for all positive integers

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Q: 3. The v77 is between what two integers?

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Q: Let x be a real number. Prove by contrapositive that if x + 5x = 40, then x < 3.

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Q: a. On each of four consecutive plays in a football​ game, a team lost 8 yards. If lost yardage is…

A: On each of  four consecutive Plays in football gane team lost 8 yards

Q: Which of the following is an Integer ?

A: Given,           Ingeger number.

Q: show that () is an even number.

A:

Q: Let m and n be positive integers.

A: Given, m and n be positive integers.  To prove that mℤ⊕nℤ is an ideal of ℤ⊕ℤ and that…

Q: State whether each conjecture is true or false.give a counterexample for any false conjecture For…

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Q: There is no integer that has a reciprocal that is an integer.

A: As per the instructions, we will be answering only the first question. For (32), Notice that the…

Q: Express the following using factorials: 10 x 9 x 8 x 7

A: Meaning of factorial of a natural number : Suppose n is a natural number then meaning of n! is…

Q: Let x be a real number. Prove by contrapositive that if æ + 7x = 90, then x < 4.

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Q: Let be a prime number (integer). Show that p2 + 5 cannot be a prime number.

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Q: Show that in any collection of 7 or more natural numbers there are ALWAYS TWO numbers whose sum or…

A: In the given problem we have to show that in any collection of 7 or more natural numbers there are…

Q: Let x be a real number. Prove by contrapositive that if x' + 7x = 90, then x < 4.

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Q: Prove that √7 is an irrational number.

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Q: Show that 2 is a primitive root of 19.

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Q: 6. Let a be a real number.

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Q: Use a direct proof to show that if x is a real number such that (x – 1)? = 0, then x³ –1 = 0.

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