Question

what are the converse, inverse, contrapositive, and biconditional of the following conditional? if the animal is a bird, then the animal has wings. 1. converse: exchange the hypothesis and conclusion. if the animal has wings, its a bird. 2. inverse: put “not” in both the hypothesis and conclusion. if the animal does not have wings, its not a bird. 3. contrapositive: put “not” in both the hypothesis and conclusion and exchange the hypothesis and conclusion. if its not a bird, it does not have wings. 4. biconditional: put “if and only if” between the hypothesis and the conclusion. envision™ geometry • teaching resources

Explanation:

1. Converse: By swapping the hypothesis "the animal is a bird" and the conclusion "the animal has wings", we get "If the animal has wings, then the animal is a bird".
2. Inverse: Adding "not" to both the hypothesis and conclusion of the original conditional, we have "If the animal is not a bird, then the animal does not have wings".
3. Contrapositive: First, add "not" to both parts and then swap them. So from the original, we get "If the animal does not have wings, then the animal is not a bird".
4. Biconditional: Inserting "if and only if" between the hypothesis and conclusion gives "The animal is a bird if and only if the animal has wings".

Answer:

1. Converse: If the animal has wings, then the animal is a bird.
2. Inverse: If the animal is not a bird, then the animal does not have wings.
3. Contrapositive: If the animal does not have wings, then the animal is not a bird.
4. Biconditional: The animal is a bird if and only if the animal has wings.