Question

question 3
which of the following are true when interpreting the \all\ statement? select all that apply.
all even numbers are divisible by two.
□ some even numbers are divisible by three.
□ if a number is even, then it is not divisible by two.
□ if a number is even, it must be divisible by two.
□ no even numbers are divisible by two.
□ there are no even numbers that are not divisible by two.
□ all prime numbers are not divisible by two.

Explanation:

1. "Some even numbers are divisible by three": True (e.g., 6, 12 are even and divisible by 3), and this does not contradict the original "all even numbers are divisible by two" statement.
2. "If a number is even, then it is not divisible by two": Directly contradicts the original statement, so false.
3. "If a number is even, it must be divisible by two": This is a direct restatement of the original "all" statement, so true.
4. "No even numbers are divisible by two": Directly contradicts the original statement, so false.
5. "There are no even numbers that are not divisible by two": This is logically equivalent to the original statement (all even numbers are divisible by two means there are no exceptions), so true.
6. "All prime numbers are not divisible by two": False, because 2 is a prime number that is divisible by two.

Answer:

• Some even numbers are divisible by three.
• If a number is even, it must be divisible by two.
• There are no even numbers that are not divisible by two.