Question

which statement explains why the value of (lfloor 2.4
floor) is 2 but the value of (lfloor -2.4
floor) is (-3)?

• because 2 is the greatest integer not greater than 2.4, and (-3) is the greatest integer not greater than (-2.4)
• because 2.4 rounds to 2, and (-2.4) rounds to (-3)
• because 2.4 is positive, and (-2.4) is negative
• because 2 is the least integer greater than 2.4, and (-3) is the least integer greater than (-2.4)

Explanation:

The notation $\lfloor x
floor$ represents the floor function, which is defined as the greatest integer that is less than or equal to (not greater than) $x$. For positive 2.4, the greatest integer not greater than it is 2. For negative -2.4, integers not greater than it include -3, -4, etc., so the greatest one is -3. The other options are incorrect: rounding -2.4 would give -2, sign alone does not explain the floor value, and the last option describes a ceiling function, not floor.

Answer:

because 2 is the greatest integer not greater than 2.4, and -3 is the greatest integer not greater than -2.4