Can some one give me a statement and its Inverse converse and contrapositive?

Question

Please make it simple and preferrably referring to common cartoons or disney characters

Answer 1

Conditional: If Goofy dated Minnie, then Mickey would be jealous.

Converse: If Mickey would be jealous, then Goofy dated Minnie.

(put the second part (the then) in the front, and the first part (the if) in the second part

Inverse: If Goofy didn't date Minnie, then Mickey wouldn't be jealous.

(keep it like the conditional but just put the opposite like if it says would in the conditional put wouldn't on each side)

Contrapositive: If Mickey wouldn't be jealous, then Goofy didn't date Minnie.

(change everything, reverse the sentence like the converse and put the opposite in front like the inverse)

i hope this helps laur!! i love these i can actually understand them!!

Answer 2

I'll give you two ot them

Let A be the car is a Mustang
let B be that the car is a Ford

(you do know that Mustang is made by Ford, right?)

So,

statement: if it's a mustang then it's a ford:
A -> B

contrapositive, if it's not a ford then it's not a mustang:
not B -> not A

A statement and it's contrapositive are equivalent: This means that :

(A->B) <--> (not B ->not A)

This is commonly called and 'if and only if' or iff. When proving and iff, you do two proofs: going in the two directions.

Frequently it's easier to prove the contrapositive of a statement than the statement itself. The about means that they are equivalent.


Try to find inverse here:
http://en.wikibooks.org/wiki/Mathematical_Proof/Introduction/Logical_Reasoning

Answer 3

A. The cartoon is Bugs Bunny.
B. The cartoon is a bunny.

Statement: A → B:
If the cartoon is Bugs Bunny, then the cartoon is a bunny.

Inverse, ~A → ~B:
If the cartoon is not Bugs Bunny, then the cartoon is not a bunny. (This is not logically equivalent to the original statement)

Converse: B → A:
If the cartoon is a bunny, then the cartoon is Bugs Bunny. (This also is not logically equivalent to the original statement)

Contrapositive: ~B → ~A
If the cartoon is not a bunny, then the cartoon is not Bugs Bunny. (This, on the other hand, is logically equivalent to the statement)

Answer 4

statement :
IF you are a duck AND you are rich THEN your name is dagobert duck.


inverse statement
IF you are not a duck OR you are NOT rich THEN your name is NOT dagobert duck.

( well i assume here that only characters from disney world are allowed. )
the negation of ' A AND B ' is 'NOT A OR NOT B'

Contrapositive :
IF you name is NOT dagobert duck THEN you are not a duck OR you are NOT rich.

( IF A THEN B becomes if NOT B then NOT A )

Answer 5

[1] I live in LA then I live in CA then
[2] I live in CA, then I live LA ( CONVERSE )
[3] I do NOT live in LA , then I do NOT live in CA ( INVERSE )
[4] I do NOT live in CA , then I do NOT live in LA
( CONTRAPOSITIVE)
If [1] is true then [2] , [3] are false and [4] is true as [1]