The correct answer is: No, it is not. When the definition is separated into two conditional statements, both of the statements are false.
The statement "An integer is divisible by 100 if and only if its last two digits are zeros" is not a good definition because it is not accurate. While it is true that all integers with last two digits as zeros are divisible by 100, there are other integers with different last two digits that are also divisible by 100 (e.g. 200, 300, etc.). Thus, the statement does not cover all possible cases and is therefore incomplete.
Is the following statement a good definition? Why? An integer is divisible by 100 if and only if its last two digits are zeros. No, it is not. When the definition is separated into two conditional statements, one of the statements is false. No, it is not. When the definition is separated into two conditional statements, both of the statements are false. Yes, it is. When the definition is separated into two conditional statements, one of the statements is true. Yes, it is. When the definition is separated into two conditional statements, both of the statements are true.
1 answer
1 answer