Question

N is an odd number.

Which statements are true?
You must get them all correct to get any marks.
A: n - 1 is odd
B: n(n − 1) is odd
C: (n-1)? is odd D: 2 + 2 is odd
E: n(n-2) is odd F: (n - 2)2 is odd

Answer 1

None of the statements are true when n is an odd number because each statement either incorrectly characterizes an even result as odd or mischaracterizes the parity of the result of the operations involving n.

Step-by-step explanation:

If n is an odd number, the following statements can be evaluated for their truth:

• A: n - 1 is odd. This statement is false. When subtracting 1 from an odd number, the result is always even.
• B: n(n − 1) is odd. This statement is false. Since n is odd and n-1 is even, their product is even.
• C: (n-1)2 is odd. This statement is false. The square of an even number, which is what (n-1) would be, is also even.
• D: 2 + 2 is odd. This statement is false. The sum of 2 + 2 is 4, which is an even number.
• E: n(n-2) is odd. This statement is false. Since n is odd, (n-2) would be odd too, and the product of two odd numbers is odd. However, the given statement claims it is odd, which is a contradiction.
• F: (n - 2)2 is odd. This statement is false. As with (n-1)2, this is also the square of an odd number (since n is odd), and therefore the result is odd.

Therefore, none of the statements A through F are true when n is an odd number.

Answer 2

E: n(n-2) is odd F: (n - 2)2 is odd

Step-by-step explanation:

Odd numbers are numbers divisible by 2 [ 1, 3, 5, 7, 9 … ]

» Assume n is 3

`{ \tt{n - 1 = 3 - 1 = 2 \: \{even \: number \}}} \\ { \tt{n(n - 1) = 2 * 3 = 6 \: \{even \: number \}}} \\ { \tt{n(n - 2) = 3(3 - 2) = 3 \: \: \{odd \: number \}}}`