Final answer:
Option a) 6 ÷ 3 is a counterexample to the incorrect statement that the quotient of an even number and an odd number will never be an integer, as dividing 6 by 3 results in the integer 2.
Step-by-step explanation:
The question seeks a counterexample to the statement that the quotient of an even number and an odd number will never be an integer. Let's examine each option:
- a) 6 ÷ 3: Here, 6 is an even number and 3 is an odd number. When we calculate the division, 6 divided by 3 equals 2, which is an integer. Therefore, this is a counterexample to the statement and demonstrates that an even number divided by an odd number can indeed result in an integer.
- b) 8 ÷ 5: 8 divided by 5 is not an integer, as the result is 1.6.
- c) 4 ÷ 3: Similarly, 4 divided by 3 does not result in an integer, as the result is approximately 1.33.
- d) 10 ÷ 2: Although 10 is an even number and 2 is an odd number, since 2 is also a divisor of 10, the result of this division is 5, which is an integer. However, because 2 is not an odd number, this scenario does not apply to the statement we're trying to disprove.
Therefore, the correct counterexample to the statement is option a), 6 ÷ 3.