Is the following statement a good definition? Why? An integer is divisible by 100 if and only if its last two digits are zeros.
Yes, it is. When the definition is separated into two conditional statements, both of the statements are true. No, it is not. When the definition is separated into two conditional statements, one of the statements is false. Yes, it is. When the definition is separated into two conditional statements, one of the statements is true. No, it is not. When the definition is separated into two conditional statements, both of the statements are false.
The given statement is: An integer is divisible by 100 if and only if its last two digits are zeros
The two conditional statements that can be made are:
1) If an integer is divisible by 100 its last two digits are zeros.
This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have last two digits zeros.
2) If the last two digits of an integer are zeros, it is divisible by 100.
This is also true. If last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.
Therefore, the two conditional statements that are formed are both true.
So, the option A is the correct answer. Yes, it is. When the definition is separated into two conditional statements, both of the statements are true
