العلاقات في المثلث: البرهان غير المباشر- حل مسائل

The video tutorial explains how to use indirect proof to show that if the square of an integer is odd, then the integer itself must be odd. The process involves assuming the opposite of the conclusion, representing it mathematically, and deriving a contradiction. This contradiction confirms the original statement is true, thus completing the indirect proof.

What is the main goal of the indirect proof discussed in the video?

• To prove that even numbers have odd squares.

• To prove that all integers are odd.

• To prove that if the square of an integer is odd, the integer is odd.

• To prove that the square of an integer is even.

What assumption is made in the indirect proof method?

• The integer is even.

• The integer is prime.

• The integer is odd.

• The integer is negative.

How is an even integer expressed in the proof?

• As 3k, where k is an integer.

• As 2k + 1, where k is an integer.

• As 2k, where k is an integer.

• As k^2, where k is an integer.

What contradiction arises from assuming the integer is even?

• The square becomes a prime number.

• The square becomes an odd number.

• The square becomes an even number.

• The square becomes a negative number.

What conclusion is reached at the end of the proof?

• The integer is both odd and even.

• The original statement is false.

• The original statement is true.

• The integer is neither odd nor even.