What’s the contrapositive of the statement “A rectangle R with side lengths 1 and x, where x is rational, cannot be tiled by finitely many squares.” Is the statement “If a rectangle R can be tiled by finitely many squares, then the side lengths are 1 and x, where x is a rational number” is correct? Or is it “If a rectangle R can be tiled by finitely many squares, then the side lengths are not 1 and x, where x is a rational number.”?

Q: 4. Solve. A) 3 ()² − 7 (¹) + 4 = 0

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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Q: If a and b are integers, then a/b is always a rational number. True False

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Q: Show that √2 + √3 is irrational.

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Q: write down the proof of the statement " √2 + √5 is not rational" in latex

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Q: 6. Prove that the statement "If x is a real number such that x² > 4 then x > 2" is false.

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A: Irrational numbers cannot be negative.

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A: We have to write the converse, inverse and contrapositive of the statement

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A:

Q: se a dire tional.

A: Introduction: A direct proof is a logical series of statements that demonstrate the truth or falsity…

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Q: All rational number are real numbers. 1/2 is a fraction number there fore 1/2 is real numbers .  Q…

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Q: A) (1 + √₂)² B) (1 -√2)² c)(1+√2)(1+√-2) D)(1+√2)(1-√√2) E)√2² + (√2)² Which of the above…

A: A) 1+22B) 1-22C) 1+21+2D) 1+21-2E) 22+22

Q: Prove that there do not exist two rational numbers whose sum is irrational.

A: prove of this question is given below...

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A: We have to find the number of non negative integer solution of Note: According to the guidelines we…

Q: If m and n are rational numbers such that √m +√n = √5+√24 ,calcule a possible value for m² + n²

A: Given that √m +√n = √5+√24 To calcule a possible value for m² + n²

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Q: 3. In the domain of real numbers, explain what the following statement says in English. A rational…

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Q: (a) Vx(x² > 4 →x>-2). (b) Vx3y (2x + y² = 0). (c) Vxy(x² + y = 25). (d) 3xy(x² + y² = -1).

A: a False b False c True d False

Q: 7) The perimeter of a square is 16x²-12y Find an expression for the length of each side. ( [atnioq…

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Q: . Classify as rational or irrational. • 8/9 • √3/4 • 49 • √6 •³√8

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Q: For any integers a and b, a + b ≥ 15 implies that a ≥ 8 or b ≥ 8.

A: Let a+b≥15, where a,b are integers.   Case 1: b<8 Then: b<8⇒-b>-8⇒15-b>15-8⇒a≥15-b>7…

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Q: 6. Prove that x is a rational number if and only if 2x - 1 is a rational number.

A: To Prove: x is a rational number if and only if 2x-1 is a rational number.

Q: How do I prove that if a,b are rational numbers, then so is (a+b)/2

A: If a,b are two rational numbers, then we have to prove thata+b2 is also a rational number.

Q: 1. Solve the polynomial inequalities a) x2 - 7x + 12.>0 b) x3 + 4x2 -3

A: The solution are next step

Q: Prove that 3+√3 is irrational.

A: As per guidelines we are supposed to solve the maximum one questions at  a time kindly post another…

Q: 4. Prove the statement: If X is rational and xy is irrational, then y is irrational.

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Q: Prove the associative property af the rational numbers (Q) a

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.