How do I conclude this Lewis Carroll discrete math problem N

How do I conclude this Lewis Carroll discrete math problem?

No interesting poems are unpopular among people of real taste

No modern poetry is free from affectation

All your poems are on the subject of soap bubbles

No affected poetry is popular among people of real taste

No ancient poem is on the subject of soap bubbles

Solution

The universe in this puzzle is the collection of all poems, while the five assertions are implications involving the simpler statements

I : it is interesting

,

P : it is popular among people of real taste

M : it is modern

,

A : it is affected

Y : it is your poem

,

S : it is on the subject of soap bubbles .

Again, we write each statement symbolically, along with its contrapositive:

(a)   I P

,

~P ~I

(b)   M A

,

~A ~M

(c)   Y S

,

~S ~Y

(d)   A ~P

,

P ~A

(e)   ~M ~S

,

S M .

If we begin with the letter I we produce the chain

I P ~A ~M ~S ~Y ,

and if we begin with the letter Y we create the contrapositive chain,

Y S M A ~P ~I .

Thus the solution to the puzzle is I ~Y, or the equivalent contrapositive Y ~I.

The simplest translation back into words is perhaps the cruel statement

“All Your Poems are Uninteresting”