Question

Which number sentence is not true?

A) |–1 >1/2
B) [1]= -1
C) [1/2] < [-1]
D) [-1/2] < [-1]

Answer 1

Option B) [1] = -1 is the number sentence that is not true because the greatest integer less than or equal to 1 is 1 itself, not -1.

Step-by-step explanation:

To determine which number sentence is not true, we must evaluate each option:

• A) |–1| > 1/2 is not true because the absolute value of –1 is 1, and 1 is indeed greater than 1/2.
• B) [1] = -1 is not true because the square brackets typically denote some form of function or operation, such as the greatest integer function (also known as the floor function) that returns the largest integer less than or equal to a number. Since 1 is an integer, [1] should be equal to 1, not -1.
• C) [1/2] < [-1] is true if we are using the floor function because the floor of 1/2 is 0 and the floor of -1 is -1, and 0 is indeed greater than -1.
• D) [-1/2] < [-1] is true because the floor of -1/2 is -1 and the floor of -1 is -1 as well, making them equal, which means the inequality holds.

Thus, the number sentence that is not true is B) [1] = -1.