Which of the following is a valid proof for the statement: If n is an even integer, then n^2 is even?
Correct Answer: If n = 2k, then n^2 = (2k)^2 = 4k^2, which is even.
- Step 1: Understand what an even integer is. An even integer can be written as n = 2k, where k is any integer.
- Step 2: Substitute n in the expression n^2. If n = 2k, then n^2 = (2k)^2.
- Step 3: Calculate (2k)^2. This equals 4k^2.
- Step 4: Recognize that 4k^2 is even. Since 4 is an even number and multiplying it by any integer (k^2) will also result in an even number.
- Step 5: Conclude that if n is an even integer, then n^2 is also even.
No concepts available.
