Practice In Immediate Inference
Put each of the following into standard form, and then find the contrapositive, obverse, converse and contradictory of each of the following, and state whether each is logically equivalent to the original.
1. Virtually every cracker in this box was round.
2. Every day I have the blues.
3. Some cats don't like rats.
4. No news is good news.
5. I'd like the world to sing in perfect harmony.
6. Sometimes I'm happy.
7. My disposition depends on you.
8. I've got the world on a string.
9. Mimi owns a moo-moo.
10. Not a single renegade was in the light brigade.
11. I ain't got nothin'.
12. We are two wild and crazy guys.
ANSWERS:
NOTE RE: ANSWERS: There are different ways to word correct answers, so your answers need not be worded exactly the same as what follows in order to be correct. If you're not sure if an answer you have is correct you should ask the instructor.
1. Virtually every cracker in this box was round.
standard form: Some crackers in this box are round things.
contrapositive: Some non-round-things are non-crackers-in-this-box. Not equivalent.
obverse: Some crackers in this box are not non-round-things. Equivalent.
converse: Some round things are crackers in this box. Equivalent.
contradictory: No crackers in this box are round things. Not equivalent.
2. Every day I have the blues.
standard form: All days are days I have the blues.
contrapositive: All non-days-I-have-the-blues are non-days. Equivalent.
obverse: No days are non-days-I-have-the-blues. Equivalent.
converse: All days I have the blues are days. Not equivalent.
contradictory: Some days are not days I have the blues. Not equivalent.
3. Some cats don't like rats.
standard form: Some cats are not things that like rats.
contrapositive: Some non-things-that-like-rats are non-cats. Equivalent.
obverse: Some cats are non-things-that-like-rats. Equivalent.
converse: Some things that like rats are not cats. Not equivalent.
contradictory: All cats are things that like rats. Equivalent.
4. No news is good news.
standard form: No things that are news are things that are good news.
contrapositive: No non-things-that-are-good-news are non-things-that-are-news. Not equivalent.
obverse: All things that are news are non-things-that-are-good-news. Equivalent.
converse: No things that are good news are things that are news. Equivalent.
contradictory: Some things that are news are things that are good news. Not equivalent.
5. I'd like the world to sing in perfect harmony.
standard form: All things that are me are things that would like the world to sing in perfect harmony.
contrapositive:
All non-things-that-would-like-the-world-to-sing-in-perfect-harmony are non-things-that-are-me. Equivalent.obverse:
No things that are me are non-things-that-would-like-the-world-to-sing-in-perfect-harmony. Equivalent.converse: All things that would like the world to sing in perfect harmony are things that are me. Not equivalent.
contradictory: Some things that are me are not things that would like the world to sing in perfect harmony. Not equivalent.
6. Sometimes I'm happy.
standard form: Some times are times that I'm happy.
contrapositive: Some non-times-that-I'm-happy are non-times. Not equivalent.
obverse: Some times are not non-times-that-I'm-happy. Equivalent.
converse: Some times that I'm happy are times. Equivalent.
contradictory: No times are times that I'm happy. Not equivalent.
7. My disposition depends on you.
standard form: All things that are my disposition are things that depend on you.
contrapositive: All non-things-that-depend-on-you are non-things-that-are-my-disposition. Equivalent.
obverse: No things that are my disposition are non-things-that-depend-on-you. Equivalent.
converse: All things that depend on you are things that are my disposition. Not equivalent.
contradictory: Some things that are my disposition are not things that depend on you. Not equivalent.
8. I've got the world on a string.
standard form: All things that are me are things that have the world on a string.
contrapositive: All non-things-that-have-the-world-on-a-string are non-things-that-are-me. Equivalent.
obverse: No things that are me are non-things-that-have-the-world-on-a-string. Equivalent.
converse: All things that have the world on a string are things that are me. Not equivalent.
contradictory: Some things that are me are not things that have the world on a string. Not equivalent.
9. Mimi owns a moo-moo.
standard form: All things that are Mimi are things that own a moo-moo.
contrapositive: All non-things-that-own-a-moo-moo are non-things-that-are-Mimi. Equivalent.
obverse: No things that are Mimi are non-things-that-own-a-moo-moo. Equivalent.
converse: All things that own a moo-moo are things that are Mimi. Not equivalent.
contradictory: Some things that are Mimi are not things that own a moo-moo.
10. Not a single renegade was in the light brigade.
standard form: No renegades are things in the light brigade.
contrapositive: No non-things-in-the-light-brigade are non-renegades. Not equivalent.
obverse: All renegades are non-things-in-the-light-brigade. Equivalent.
converse: No things in the light brigade are renegades. Equivalent.
contradictory: Some renegades are things in the light brigade. Not equivalent.
11. I ain't got nothin'.
standard form: No things that are me are things that have something.
contrapositive: No non-things-that-have-something are non-things-that-are-me. Not equivalent.
obverse: All things that are me are non-things-that-have-something. Equivalent.
converse: No things that have something are things that are me. Equivalent.
contradictory: Some things that are me are things that have something. Not equivalent.
12. We are two wild and crazy guys.
standard form: All things that are us are two wild and crazy guys.
contrapositive: All non-two-wild-and-crazy-guys are non-things-that-are-us. Equivalent.
obverse: No things that are us are non-two-wild-and-crazy-guys. Equivalent.
converse: All things that are two wild and crazy guys are things that are us. Not equivalent.
contradictory: Some things that are us are not two wild and crazy guys. Not equivalent.
