Suppose x and y are any integers. Prove that if x and y are odd, then x+ 5y² is even

Q: Prove that if a is an odd integer, then 5a² – 3a + 5 is odd.

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Q: Prove that if x is a positive real number, then LV L]] = [V]

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Q: let b be a nonzero integer. prove that gcd (0,b) = |b|.

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Q: If all entries of A are integers, and det A = 1 or -1, prove that all entries of A -1 are integers.…

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Q: If x is an odd integer, then x² +3x+5 is odd.

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Q: Prove that for all integers a, b, and c if a divides b - 1 and a divides c - 1 then a divides bc…

A: If a number x divides y then y is a multiple of x.

Q: Suppose x and y are any integers. Prove that if x and y are odd, then x + 5y is even

A: Suppose x and y are odd integers. To show x+5y2 is even. Note: Square of an odd number is odd.…

Q: Let a, b eN. Prove that if a + b is even, then there exists nonnegative integers x and y such hat x²…

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Q: Prove or disprove if x2-1 is odd, then x is even

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Q: Prove that for every positive integer m, there is a positive integer k such that k does not divide m…

A: Given:-                 prove that every positive integer m, there is a positive integer K such that…

Q: Let x and y be integers. Prove that if x2 - y2 is even, then x + y is odd

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Q: 3. Prove by contradiction, that if x and y are odd integers, then there is no integers z such that…

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Q: Prove by contrapositive. if x and y are integers such that x > 1, and x divides y, then x / (y +1)

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Q: For every pair of integers x and y, if x – y is odd, then x is odd or y is odd.

A: Let x-is even integer and y-is even integer. x=2m, y=2n

Q: If all entries of A and A -1 are integers, prove that <let A = 1 or -1. Hint: What is det A times…

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Q: Let a, y E R. Prove that if 21a + 35y = 45, then a and y are not both integers.

A: An integer is colloquially defined as a number that can be written without a fractional component.…

Q: Prove that if m is a positive integer and r is a real number, then Lma) = l=] + -+ + + [-+ + r+ m

A: We are given a Inequality involving the sum of floor functions, and we have to prove that.

Q: Prove that for every integer x, x+4 is odd if and only if x+7 is even

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Q: There exists an integer x>0, such that for all integers y>0, there exists an integers z>0, so that…

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Q: If α is even, prove that α-1 is even. If α is odd, prove that α-1 is odd.

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Q: If a and b are distinct integers prove that a-b is a factor of an -b" whenever n is positive integer

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Q: Prove that if x is an even integer, thenx^2−6x+ 3is odd

A: Any integer of the form 2m+1 is odd.

Q: prove that if a and b are both odd integers, then ab+1 is an even integer

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Q: Let x and y be integers. Prove by the contrapositive that if x2 - y2 is even, the x + y is even

A: Let x and y be integers such that x2-y2 is even. We have to prove that x+y is even. Suppose that x+y…

Q: . Use direct proof to prove that, if x is a positive odd integer, then z – 1 is wholly dividable у…

A: x^2-1 is divisible by 4.

Q: If a and b are nonzero integers and m is the least common multiple of a and b, prove that (a) ∩ (b)…

A: Consider the given statement. (a) ∩ (b) = (m) Consider the left side of the equation. As, m is the…

Q: Prove that if the product of two integers qs is odd, then q2 + s2 is even. Then show that for…

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Q: Prove that if x is a real number, then [2x] = [x] +

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Q: Prove that if ∣A∣ = 1 and all entries of A are integers, then all entries of ∣A−1∣ must also be…

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Q: Prove that the difference between two integers is odd if and only if exactly one of the integers is…

A: Suppose x be any integer. If x is odd then x=2m+1 for some integer m. If x is even then x=2m for…

Q: 4. Demonstrate that for positive integers t and Q, (t <= [V@]) is equivalent to (t x t <= Q). Show…

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Q: there are no integers x and y such that x is a prime greater than 5 and x=6y+3

A: Given query is to check the statement whether it's possible or not.

Q: Prove that x + 3 is odd if and only if x² is even.

A: Proof: x+3 is odd  Let x+3 = 2k+1

Q: Prove: If a is a positive even integer and b is an odd integer, then (a,b)=(a/2, b).

A: Let d be gcd of a and b. Now, b is odd so d cannot be even or is odd.  Now, since d is odd and…

Q: Let a and b be integers which are not both zero, and let d= gcd(a, b). Prove that gcd (a/d,b/d)= 1.

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Q: Prove the following by contrapositive: If x is an even integer, then x^2 is even.

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Q: Suppose A and B are bounded and nonempty subsets of real numbers and 1 E R. In this case: sup(AB) =…

A: Suppose A and B are bounded and nonempty subsets of real numbers and λ∈R. We need to prove that…

Q: Prove that if a and b are real numbers with a < b, then there are infinitely many rational numbers…

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Q: Suppose that c is a positive integer. Define f(c) to be the number of pairs (a, b) of positive…

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Q: Select each step to complete a proof by contrapositive of the theorem below. Theorem: For every pair…

A: Here we have to prove the theorem that “For every pair of integers x and y, if 5xy + 8 is even, then…

Q: Prove that for integers a and b, (a -3)b2 is even if and only if a is odd or b is even.

A: We need to prove that for integers a and b, (a -3)b^2 is even if and only if a is odd or b is even.

Q: Prove that ifx^2−6x+ 3is odd, then x is even

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Q: and

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Q: Prove that if m is a positive integer and x is a real number, then [m2] = [=] + z++ + 2 + |x + т — 1…

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Quadratic Equation

When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.

Demand and Supply Function

The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.