I need a reference to check and see if my work is correct. THANKS!!! Question: S

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I need a reference to check and see if my work is correct. THANKS!!!

Question:

State the converse and the contrapositive of each of the following sentences. Be sure to label each.

(a) In order for it to rain it is necessary that there be clouds.
(b) In order for it to rain it is sufficient that there be clouds.
(c) If life is a bowl of cherries then I am not in the pits.
(d) If I am not a fool then mares eat oats.
(e) A sufficient condition for the liquidity of water is that the temperature exceeds 32 degrees Fahrenheit.
(f) A necessary condition for peace in the world is that all people disarm.
(g) What's good for the goose is good for the grander.
(h) If wishes were horses then beggars would ride.
(i) If my grandmother had wheels, she'd be a garage truck.
(j) If he won't play ball then he's benched.
(k) If the Donald won't buy it then it's not worth a dime.
(l) If Marla wants it then the Donald will buy it.

THANKS!!!

Explanation / Answer

For conditional statement "If A, then B," the converse is "If B, then A," and the contrapositive is "If not B, then not A." If the statement is not in "If A, then B" format, we rephrase it. a) Equivalent to, "If it is raining, then there are clouds." Converse: "If there are clouds, then it is raining." Contrapositive: "If there are no clouds, it cannot rain." b) Equivalent to, "If there are clouds, then it is raining." Converse: "If it is raining, then there are clouds." Contrapositive: "If it is not raining, then there are no clouds." c) Converse: "If I am not in the pits, then life is a bowl of cherries." Contrapositive: "If I am in the pits, then life is not a bowl of cherries." d) Converse: "If mares eat oats, then I am not a fool." Contrapositive: "If mares don't eat oats, then I am a fool." e) Equivalent to, "If the temperature exceeds 32 degrees Fahrenheit, then water is a liquid." Converse: "If water is a liquid, then the temperature exceeds 32 degrees Fahrenheit." Contrapositive: "If water is not a liquid, then the temperature does not exceed 32 degrees Fahrenheit." f) Equivalent to, "If there is peace in the world, then all people have disarmed." Converse: "If all people have disarmed, then there is peace in the world." Contrapositive: "If not all people have disarmed, then there is not peace in the world." g) Equivalent to, "If it's good for the goose, then it's good for the gander." (It says "grander;" I think they mean "gander.") Converse: "If it's good for the gander, then it's good for the goose." Contrapositive: "If it's not good for the gander, then it's not good for the goose." h) Converse: "If beggars are riding, then wishes are horses." Contrapositive: "If beggars are not riding, then wishes are not horses." i) (Says "garage truck," I think it must mean "garbage truck.") Converse: "If my grandmother is a garbage truck, then she has wheels." Contrapositive: "If my grandmother is not a garbage truck, then she does not have wheels." j) Converse: "If he's benched, then he wouldn't play ball." Contrapositive: "If he's not benched, then he will play ball." k) Converse: "If it's not worth a dime, then Donald won't buy it." Contrapositive: "If it's worth a dime, then Donald will buy it." l) Converse: "If Donald will buy it, then Marla wants it." Contrapositive: "If Donald won't buy it, then Marla doesn't want it."

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