Write the converse, inverse, and contrapositive of this conditional statement and determine whether the statement is true or false: If a number is even, then it is evenly divisble by 2.
Converse: If a number is evenly divisible by 2, then it is even.
Inverse: If a number is not even, then it is not evenly divisible by 2.
Contrapositive: If a number is not evenly divisible by 2, then it is not even.
The statement and its converse are both true.
The given conditional statement is:
"If a number is even, then it is evenly divisible by 2."
Converse:
If a number is evenly divisible by 2, then it is even.
Inverse:
If a number is not even, then it is not evenly divisible by 2.
Contrapositive:
If a number is not evenly divisible by 2, then it is not even.
Now, let's determine whether each statement is true or false.
The converse of the given statement is true because if a number is evenly divisible by 2, it is indeed even.
The inverse of the given statement is also true because if a number is not even, then it is not evenly divisible by 2.
The contrapositive of the given statement is true because if a number is not evenly divisible by 2, then it is not even.
In conclusion, all the converse, inverse, and contrapositive of the given conditional statement are true.
The given conditional statement is: "If a number is even, then it is evenly divisible by 2."
To find the converse, inverse, and contrapositive of the statement, we need to manipulate the original statement.
Converse: "If a number is evenly divisible by 2, then it is even."
To form the converse, we switch the hypothesis and the conclusion of the original statement.
Inverse: "If a number is not even, then it is not evenly divisible by 2."
To form the inverse, we negate both the hypothesis and the conclusion of the original statement.
Contrapositive: "If a number is not evenly divisible by 2, then it is not even."
To form the contrapositive, we switch and negate both the hypothesis and the conclusion of the original statement.
Now, let's determine whether these statements are true or false:
Original Statement: If a number is even, then it is evenly divisible by 2.
This statement is true, as it is a basic mathematical principle.
Converse: If a number is evenly divisible by 2, then it is even.
This statement is also true because if a number can be divided evenly by 2, it implies that the number is even.
Inverse: If a number is not even, then it is not evenly divisible by 2.
This statement is false because a number not being even does not necessarily mean it cannot be evenly divisible by 2. For example, some odd numbers are also divisible by 2.
Contrapositive: If a number is not evenly divisible by 2, then it is not even.
This statement is also false because some numbers that are not evenly divisible by 2 can still be even.
To summarize:
- The original statement is true.
- The converse is true.
- The inverse and contrapositive are false.