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We prove 0x = 0 as below. Which method of proof did we use?

 Question 1

 We prove 0x = 0 as below. Which method of proof did we use?

 X=X

 X-x = 0

 (1-1)x =0

 0x =0

  •  direct proof

  •  proof by cases

  •  proof by contrapositive


 Question 2

 If direct proof is used to prove the following statement: If x is a real number and x s 3, then 12 - 7x +

 x*x > 0. What is the hypothesis?

 12- 7x+x*x>0

 If x is a real number and xs 3

 12-7x+x*x<0

 If x is not a real number or x > 3


 Question 3

 If proof by contrapositive is used to prove the following statement: For every real number x, if x is

 irrational, then -x is also irrational. What is the hypothesis?

 -x is rational.

 x is rational.

 -x is irrational.

 x is irrational.


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Answer #1

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