I am my own grandfather problem

Many, many years ago when I was twenty-three
I was married to a widow who was pretty as could be
This widow had a grownup daughter who had hair of red
My father fell in love with her, and soon they too were wed
This made my Dad my son-in-law and really changed my life
For now my daughter was my mother, 'cause she was my father's wife
And to complicate the matter, even though it brought me joy,
I soon became the father of a bouncing baby boy
My little baby then became a brother-in-law to Dad
And so became my uncle, though it made me very sad
For if he were my uncle, then that also made him brother
Of the widow's grownup daughter, who was of course my stepmother
Father's wife then had a son who kept them on the run
And he became my grandchild, for he was my daughter's son
My wife is now my mother's mother, and it makes me blue
Because although she is my wife, she's my grandmother too
Now if my wife is my grandmother, then I'm her grandchild
And every time I think of it, it nearly drives me wild
'Cause now I have become the strangest case you ever saw
As husband of my grandmother, I am my own grandpa

CHALLENGES:
1. Write Predicate Calculus representing the situation with a series of expressions
2. Use modus ponens to conclude that “I am my own grandfather”.

First, try it out yourself!

Click here to reveal solution!

Predicate Calculus representing the situation with a series of expressions:

• married(i,w).
• mother(w,d).
• mother(d,s1).
• father(f,s1).
• father(f,i).
• father(i,s2).
• mother(w,s2).

use modus ponens on this system to prove the conclusion that “I am my own grandfather”.

1. ∀ X Y ∃ Z married(X,Z)∧mother(Z,Y)⇒ father(X,Y).
2. ∀ X Y ∃ Z father(Z,X)∧father(Z,Y)⇒ brother(X,Y).
3. ∀ X Y ∃ Z father(X,Z),mother(Z,Y)⇒ grandfather(X,Y).
4. ∀ X Y ∃ Z grandfather(X,Z)∧brother(Z,Y)⇒ grandfather(X,Y).
5. married(i,w).
6. mother(w,d).
7. mother(d,s1).
8. father(f,s1).
9. father(f,i).
10. From 1,5,6::
    married(i,w)∧mother(w,d)⇒ father(i,d).
11. From 3,7,10 ::
    father(i,d),mother(d,s1)⇒ grandfather(i,s1).
12. From 2,8,9 ::
    father(f,s1)∧father(f,i)⇒ brother(s1,i).
13. From 4,11,12 ::
    grandfather(i,s1)∧brother(s1,i)⇒ grandfather(i,i).

Hence, I'm my own grandfather.

Now, a video ;)

I'm my own Grandpa. Interesting idea, isn't it?

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