Is this really “correct” and unequivocal?

Question

For one of my elementary CS classes, we move on to the "functional logic of truth."

My question relates to translation into English. Note that ^ is AND; v is (inclusive) OR; ~ NOT. → IF

Well, we had it: "Rent is a necessary condition for staying in BUSINESS"

RENT -> BUSINESS

Whenever we evaluated everything, it was wrong. I asked the teacher why she didn’t say anything more, that “if there isn’t in the sentence then, then the antecedent is always last”

I would like to explain a little more how this is wrong. And as a suggestion is not ambiguous. Something more than "was not then, so always is."

Also note: where did the logical operator come from IF? I have never heard of such a statement, which is basically equivalent in Cish code for a==true?b:true. It is very difficult for me to grasp its use.

edit: The correct answer was

BUSINESS -> RENT

Answer 1

If you pay rent, you are not necessarily in business. Rent (->) Business.

However, if you are in business, you must pay rent. Business → Rent.

Answer 2

I think it should have been written:

BUSINESS -> RENT

"If you stay in business, you pay the rent."

P -> Q

may be indicated: "P means Q", "If P, then Q" or "Q, if P."

Answer 3

. a b, b a. , , , .

Answer 4

IF? , Cish a==true?b:true. .

"". " ?"

, , .

, , , (, , 1 = 2, , 0 ). 0 -> x , x (.. ).

, , , 1 -> 1 ( ), 1 -> 0 - false ( ).

Answer 5

!RENT -> !BUSINESS

, . ""

BUSINESS -> RENT

, .

( a -> b === (!a || b)):

!BUSINESS || RENT
RENT || !BUSINESS

, , ( ).

!(!RENT && BUSINESS)

( ).

ADDED: , . , , . , , , (.. ) , , , .

RENT || !BUSINESS
!RENT
--------
!BUSINESS

, , , , , .

RENT || !BUSINESS
BUSINESS
--------
RENT

, - , .

case, , A- > C B- > C, A || B, C:

1. !A || C
2. !B || C
3.  A || B
----------
4.  B || C  (resolve 3 and 1)
5.  C       (resolve 4 and 2)

Answer 6

"". < <20 > Y. , X Y, . "Y , X ". , X false, Y - false ", X , Y , Y , X . X , Y - false, !X => !Y, Y => X. " X Y" Y => X.

: , , . , , , , , . , , . ( , ) .

, X Y Y => X.

, : "X Y". , " X Y true " X => Y.

These two implicative (this word is now!) Relationships are dual from each other. In fact, in mathematics the form is very important: " Xis a necessary and sufficient condition for Y." This means that X => Yand Y => X, or X <=> Y. We say that Xand are Yequivalent, and we sometimes say " X if and only if Y" and sometimes abbreviate it " Xiff Y."