This is a stupid question...why are we trying both subtraction and division when the question says it is only ONE type..either subtraction or division? I am confused
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations: addition,subtraction,multiplication,or division. If 6∆3≤ 3, which of the following must be true ?
I.2∆2=0
II.2∆2=1
III.4∆2=2
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
If 6 ∆ 3 ≤ 3, then the ∆ operator is subtraction AND division.
6 - 3 = 3, which satisfies the equation
\(\frac{6}{3}\) = 2, which also satisfies the equation (2 is less than 3).
The operator cannot be addition or multiplication. 6 + 3 = 9, which is > 3. And 6 * 3 = 18, also > than 3.
Check I, II, and III.
I. 2 ∆ 2 = 0. If ∆ were only subtraction, this would be fine. 2 - 2 = 0.
But \(\frac{2}{2}\) = 1. This equation is not true when ∆ is division. Incorrect.
II. 2 ∆ 2 = 1. If ∆ were only division, this would be fine.\(\frac{2}{2}\) = 1. But when ∆ is subtraction, then 2 - 2 = 0. This equation does not hold true when ∆ is subtraction. Incorrect.
III. 4 ∆ 2 = 2. This must be true for both subtraction and division.
It holds for subtraction. 4 - 4 = 2
And it holds for division: \(\frac{4}{2}\)= 2. Correct.
Answer C