If the signs, + and `div` and the numbers, 4 and 5 are interchanged, then the correct relation is:
(p) `24 + 8 xx 4 = 20 div 5`
(q) `20 div 5 - 6 = 3 xx 30 + 4 `

Options

A. (p)
B. (q)
C. both (p) and (q)
D. neither (p) nor (q)

Answer

To solve the problem, we need to interchange the signs and numbers as specified in the question. Let's break down the steps for both statements (p) and (q).

### Step-by-Step Solution:

**Statement (p):** `24 + 8 xx 4 = 20 div 5`

1. **Interchange the signs and numbers:**
- Replace `+` with `div`
- Replace `xx` (multiplication) with `+`
- Replace `4` with `5`
- Replace `5` with `4`

This gives us: `24 div 8 + 5 = 20 + 4`

2. **Calculate the left-hand side (LHS):**
- First, perform the division: `24 div 8 = 3`
- Then, add `5`: `3 + 5 = 8`

3. **Calculate the right-hand side (RHS):**
- Perform the addition: `20 + 4 = 24`

4. **Compare LHS and RHS:**
- LHS = 8
- RHS = 24
- Since 8 ≠ 24, statement (p) is false.

---

**Statement (q):** `20 div 5 - 6 = 3 xx 30 + 4`

1. **Interchange the signs and numbers:**
- Replace `div` with `+`
- Replace `-` with `-` (no change)
- Replace `xx` (multiplication) with `div`
- Replace `5` with `4`
- Replace `30` with `5`

This gives us: `20 + 4 - 6 = 3 div 5 + 4`

2. **Calculate the left-hand side (LHS):**
- First, perform the addition: `20 + 4 = 24`
- Then, subtract `6`: `24 - 6 = 18`

3. **Calculate the right-hand side (RHS):**
- Perform the division: `3 div 5 = 0.6`
- Then, add `4`: `0.6 + 4 = 4.6`

4. **Compare LHS and RHS:**
- LHS = 18
- RHS = 4.6
- Since 18 ≠ 4.6, statement (q) is also false.

### Conclusion:
- Statement (p) is false.
- Statement (q) is false.