Question

Consider the conjecture any number disciple by 2 is also divisible by 4 is each of the numbers 12 19 22 28 30 a counterexample of the conjecture ?
Number
12 19 22 28 30
Is the number a counterexample yes or no

Answer 1

To determine if each of the numbers (12, 19, 22, 28, 30) is a counterexample to the conjecture "any number divisible by 2 is also divisible by 4," we need to check the divisibility of each number by 2 and then by 4.

1. **12**:
- Divisible by 2: Yes (12 ÷ 2 = 6)
- Divisible by 4: Yes (12 ÷ 4 = 3)
- Counterexample: No

2. **19**:
- Divisible by 2: No (19 is odd)
- Counterexample: No (since it's not divisible by 2)

3. **22**:
- Divisible by 2: Yes (22 ÷ 2 = 11)
- Divisible by 4: No (22 ÷ 4 = 5.5)
- Counterexample: Yes

4. **28**:
- Divisible by 2: Yes (28 ÷ 2 = 14)
- Divisible by 4: Yes (28 ÷ 4 = 7)
- Counterexample: No

5. **30**:
- Divisible by 2: Yes (30 ÷ 2 = 15)
- Divisible by 4: No (30 ÷ 4 = 7.5)
- Counterexample: Yes

To summarize:
- **12**: No
- **19**: No
- **22**: Yes
- **28**: No
- **30**: Yes

So, for your question, the numbers that are counterexamples to the conjecture are **22 and 30**, and the others (12, 19, 28) are not counterexamples.