Which of the following statements is false ?

Options

A. `-20-(-5)=-15`
B. `|-18|gt|-13|`
C. `23+(-31)=8`
D. Greatest negative integer is -1

Answer

To determine which of the statements is false, we need to evaluate each option step by step.

### Step 1: Evaluate Option 1
**Statement:** Negative 20 minus negative 5 equals negative 15.

**Calculation:**
- Start with the expression: \(-20 - (-5)\).
- According to the rules of integers, subtracting a negative number is the same as adding its positive counterpart. Thus, we rewrite the expression:
\[ -20 + 5 \]
- Now, we perform the addition:
- Since one number is negative and the other is positive, we subtract the smaller absolute value from the larger absolute value:
\[ 20 - 5 = 15 \]
- The sign will be that of the number with the larger absolute value, which is negative:
\[ -15 \]
- Therefore, the statement is true: \(-20 - (-5) = -15\).

### Step 2: Evaluate Option 2
**Statement:** The absolute value of negative 18 is greater than the absolute value of negative 13.

**Calculation:**
- Find the absolute values:
\[ | -18 | = 18 \quad \text{and} \quad | -13 | = 13 \]
- Now compare the two absolute values:
\[ 18 > 13 \]
- Therefore, the statement is true.

### Step 3: Evaluate Option 3
**Statement:** 23 plus negative 31 gives us 8.

**Calculation:**
- Start with the expression:
\[ 23 + (-31) \]
- Since we are adding a positive and a negative integer, we subtract the smaller absolute value from the larger absolute value:
\[ 23 - 31 \]
- Now, perform the subtraction:
\[ 31 - 23 = 8 \]
- The sign will be that of the number with the larger absolute value, which is negative:
\[ -8 \]
- Therefore, the statement is false: \(23 + (-31) = -8\).

### Step 4: Evaluate Option 4
**Statement:** The greatest negative integer is negative 1.

**Calculation:**
- The set of negative integers includes: \(-1, -2, -3, \ldots\)
- Among these, \(-1\) is indeed the largest (or least negative) integer.
- Therefore, this statement is true.

### Conclusion
After evaluating all options, we find that the false statement is:
**Option 3:** 23 plus negative 31 gives us 8.