True or false All fractions are real numbers- The elements of prime numbers are odd number- Composite numbers and prime numbers have elements in common- Real number is a part of integers - All integers are natural numbers-

Q: Sum of two different prime number is a Prime number None of the mentioned o Either Prime or…

A: Given, Sum of two different prime number is a ______

Q: 19-22 - Properties of Real Numbers Rewrite the expression using the given property of real numbers.…

A: To rewrite the expression using the given property of real numbers. 19) Commutative property of…

Q: 4.A.2. Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3…

A: Yes there is an integer that has a remainder 2 when divided by 5 and a remainder of 3 when divided…

Q: 3. A mountain is 15,967 feet above sea level, and a valley is 257 feet below sea level. What is the…

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Q: Prove or disprove formally and precisely that the product of two consecutive integers is always even…

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Q: The operation subtraction on the set of natural numbers N.

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Q: True or False? If false, give an example. 1. Real Numbers can be both Rational and Irrational. 2.…

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Q: Determine whether the given sets are binary operations under addition, subtraction, multiplication,…

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Q: ) True or False? Statement True False There are integers that are not rational numbers. There are…

A: We can answer the question as per definition of rational number and integer.

Q: A fraction is said to be “irreducible” if the numerator and denominator are relatively prime, i.e.…

A: Introduction -  Reducible -Reducible fraction is a fraction that has some common factor and can be…

Q: 2. Using Direct proof, Prove: if m is an even integer and n is an odd integer, then mn is also an…

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Q: Number As a fraction Is it rational? Yes Yes 0.2 Yes 0.3 Yes No Which of the following statements…

A: Rational number:- rational  number are the numbers which can be represented in the form of  P/q…

Q: State whether or not the following are statements. In the case of a statement, indicate if it is…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 3. A property of real numbers is given. State the property and give an example in which the property…

A: (i) Commutative Property  The commutative property states that the numbers on which we operate can…

Q: Prove Euclid's theorem: If a prime divides a product of two natural numbers, then it divides one of…

A: Euclid’s Theorem: If a prime number a divides the product bc of two integers b and c, then a must…

Q: Fermat's theorem is not true for some prime number. Select one: O True O False

A: Fermat's theorem states that if p is a odd prime number, then for any integer a, the number ap − a…

Q: 3. Formulate and prove a theorem about which numbers can be represented as the sum of 1000…

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Q: iteration 1 3 a 4,613 2,564 2,564 gcd gcd(4,613, 2,564) = Are the integers relatively prime? Yes No

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Q: True or False All prime numbers are even.

A: Given statement is  "All prime numbers are even".

Q: 6 181 元 - 15 0.8

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Q: Classify the numbers Rational Irrational Integer Whole Natural 4.2 x 10 5/3 2.5 2%

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Q: True or False. 1. All real numbers are rational 2. All irrational numbers are real 3. Some rational…

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Q: Determine the Supremum and infimum of the set. A= [(n+1)÷n : n is an element of natural numbers]

A: We can find the supremum and infimum as below

Q: Question A positive integer is 15 less than another. If 4 times the reciprocal of the smaller…

A: Here we find the integer.

Q: Difference of two distinct odd prime numbers is even and composite Select one: O True O False

A: Difference of two distinct odd prime numbers is even and composite

Q: The cost of operating a bus involves the cost of gasoline , the driver's wage and other maintenance…

A: Given query is to find operating cost of bus.

Q: State whether or not the following are statements. In the case of a statement, indicate if it is…

A: 1) FALSE   Because not all perfect squares are even numbers. Examples of which are 9, 25, 49 and 81.…

Q: a. Write a description of the even numbers that uses "2" and the word "factor." b. Write a…

A: a) the number which has prime factor 2 is a even number. b) the number which is multiple of 2 is a…

Q: .Prove that if n is an odd number then 3n + 1 is an even number. Use direct proof. 2.Prove that…

A: Given n is odd number

Q: Q) Which operations on numbers are well defined in the set of real numbers R ?     addition,…

A: To find which operations on numbers are well defined in the set of real numbers R . 1) Addition…

Q: Part A. Choose a and b, two whole numbers that are relatively prime, meaning that the numbers share…

A: part A two whole numbers which are relatively prime a = 89 b = 97 a and b both are whole numbers and…

Q: contrapositive proof. Include explanation.

A: Given that if n is an even, then 7n + 4 is an even integer.

Q: Explain the Pythagorean Theorem, its proofs and applications. Between 200-500 words

A: In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the…

Q: Prove using direct proof. Include explanation.   If n is an even integer, then 7n + 4 is an even…

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Q: Use the principle of ordinary mathematical induction to prove the well-ordering principle for the…

A: To proof the WELL ORDERING PRINCIPLE VIA INDUCTION,WE NEED TO state the principal first as,

Q: Formulate and prove a theorem about which numbers can be represented as the sum of 1000 consecutive…

A: Solution: We know that for any positive integer n, the sum 1+2+3+........+n is given by,…

Q: A property that, two consecutive positive integers are relatively prime. Consider any two…

A: Proof) Let the consecutive integers be n,n+1 Let the greatest common divisor gcd(n,n+1) = d, Hence,…

Q: Can 199 cannot be written as the sum of an even integer and two odd integers. Show prove too.

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Q: Prove the divisibility criterion of 2 and 13

A: Divisibility Criteria for 2: Any integer is divisible by 2 if and only if unit digit of the integer…

Q: Using deductive reasoning to prove the number 5 is always generated by the following method.…

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Q: True or false 1. The sum, difference, product and quotient of any two integers result to an integer…

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Q: Q)Which operations on numbers are well defined in the set of real numbers R ?     addition,…

A: According to the given information, it is required to tell which operations on numbers are well…

Q: True or False? All prime numbers are positive integers. True False

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Q: Describe the structure of the real number by writing a statement that summarizes when a real number…

A: describe the structure of the real number by writing a statement that summarizes (i) when a real…

Q: Prove or disprove that: (a) The product of an odd number with any integer is odd. (b) The sum of two…

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Q: Definition: The parity of an integer is the quality of being either even or odd. For instance, 2 has…

A: Use the method of contradiction

Q: Discrete mathematics for comuter science. Answer + why Let Xi = {2i - 1}. Then Uni=1 Xi is a) a…

A: Given Xi={2i-1} now by putting some values of i = 1, 2, 3, ......., we have X1={1}, X2={3}, X3={5},…

Q: The number of factors of prime numbers are Depends on the prime number 3 0 2 0 None of the mentioned…

A: The number of factors of a prime number is 1 and prime itself. So there are 2 factors of prime…