Write the converse, inverse, and contrapositive of the conditional statement. If an animal is a bird, then it has two eyes.
converse:
If an animal has 2 eyes, then it's a bird.
inverse:
If an animal is not a bird, then it does not have two eyes.
contrapos.:
If an animal does not have 2 eyes, then it is not a bird.
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Biconditional Statement
An animal has 2 eyes iff it's a bird
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Converse: If an animal has two eyes, then it is a bird.
Inverse: If an animal is not a bird, then it does not have two eyes.
Contrapositive: If an animal does not have two eyes, then it is not a bird.
To find the converse, inverse, and contrapositive of a conditional statement, we need to understand the components of the statement.
The original statement (conditional statement) is: "If an animal is a bird, then it has two eyes."
1. Converse: In the converse, we switch the hypothesis and the conclusion. So the converse of the statement is: "If an animal has two eyes, then it is a bird."
2. Inverse: In the inverse, we negate both the hypothesis and the conclusion. So the inverse of the statement is: "If an animal is not a bird, then it does not have two eyes."
3. Contrapositive: In the contrapositive, we switch and negate the hypothesis and the conclusion. So the contrapositive of the statement is: "If an animal does not have two eyes, then it is not a bird."
To summarize:
Original Statement: If an animal is a bird, then it has two eyes.
Converse: If an animal has two eyes, then it is a bird.
Inverse: If an animal is not a bird, then it does not have two eyes.
Contrapositive: If an animal does not have two eyes, then it is not a bird.
Remember that the converse and inverse statements are not necessarily true, but the original statement and the contrapositive have the same logical truth value.