*If there is a queen in the hand then there is an ace in the hand,*

or else if there isn't a queen in the hand then there is an ace in the hand.

There is a queen in the hand. What follows?

or else if there isn't a queen in the hand then there is an ace in the hand.

There is a queen in the hand. What follows?

---------------------------

Stop reading here if you don't want the breakdown of my answer to this (which is the correct one ofc )

As many have pointed out, the statement is phrased sort of ambiguously.

The crucial ambiguity lies with the interpretation of "or else" which is the logical operator. As the logical operator, it describes the relation between two propositional units.

A) (if there is a queen in the hand then there is an ace in the hand)

B) (if there isn’t a queen in the hand then there is an ace in the hand)

But these propositions themselves are complex units that can be further broken down into simpler units with their own operators.

The breakdown of A) is :

(p→ q) or “if p) (queen) then there is q (ace)”

The breakdown of B) is

(~p→q) or “if not p (queen) then there is q (ace)”

I am going to try and explain why I believe very strongly the answer is "no ace."

There are three relevant logical operators that “or else” seems to be commonly interpreted as.

**1) [⊕] Exclusive disjunction (exclusive “or”) :**Exclusive disjunction is an operation on two logical values, typically the values of two propositions, that

**produces a value of**

**true****if**

**one but not both of its operands is true**.

**2) [V] Logical disjunction (inclusive “or”) :**Logical disjunction is an operation on two logical values, typically the values of two propositions, that

**produces a value of**

**true****if at least one of its operands is true.**

3) [^] Logical conjunction (“and”) :Logical conjunction is an operation on two logical values, typically the values of two propositions, that

3) [^] Logical conjunction (“and”) :

**produces a value of**

**true****if both of its operands are true.**

1) I am only going to talk about the exclusive disjunction in my OP. It is in my opinion the best interpretation of “or else.” which typically suggests two alternatives one of which will occur and the other will not. If it were just “or” then 2) would perhaps be a stronger interpretation, but “else” seems to me to be added commonly to denote exclusivity. For example :

1) I am only going to talk about the exclusive disjunction in my OP. It is in my opinion the best interpretation of “or else.” which typically suggests two alternatives one of which will occur and the other will not. If it were just “or” then 2) would perhaps be a stronger interpretation, but “else” seems to me to be added commonly to denote exclusivity. For example :

“

**(**

**Give me that donut)**

**or else (**

**I will kill you.)**

**” This threat only makes sense because you understand that if you give me the donut, then I will not kill you, but if you don’t give me the donut then you will die. If this operator is in play, you**

__know__that if you make one operand true, then the other operand is

**necessarily false****. The overall statement gives a value of TRUE if one but NOT BOTH of the operands are true.**

(You love it) or else (you hate it)

(the sun is out) or else (it is raining)

(My unicorn is pink) or else (Macron has a massive head)

*((If there is a queen in the hand then there is an ace in the hand,)*

or else (if there isn't a queen in the hand then there is an ace in the hand.))

There is a queen in the hand. What follows?

Now I am going to talk about truth tables and specifically the exclusive disjunction operator. I will detail the steps for how one fills in a truth table during my explanation.

1) this is my prepared truth table. What we first need to do is give the truth value for the operators and operands within the complex propositions A) and B)

or else (if there isn't a queen in the hand then there is an ace in the hand.))

There is a queen in the hand. What follows?

Now I am going to talk about truth tables and specifically the exclusive disjunction operator. I will detail the steps for how one fills in a truth table during my explanation.

1) this is my prepared truth table. What we first need to do is give the truth value for the operators and operands within the complex propositions A) and B)

*First step is to fill in all the combinatory possibilities for the operands.*

*Second step is to determine the truth value of the overall statement In A) and in B) respectively In this case: (*

*→*

*) your basic*

**implication which produces a value of****false****if the first operand is true and the second operand is false, and a value of****true****otherwise.**

Feel free to check the work according to the rule I just stated.Feel free to check the work according to the rule I just stated.

**
**

As we mentioned earlier, The rule for [⊕]

**Now comes the REALLY EXCITING BIT !!!!!**

We will fill in the truth value for the overall statement, that is (A) ⊕ B)) . The important truth values to compare are in columns 2 and 6 (circled), because that is the truth values of individual propositions A) and B)We will fill in the truth value for the overall statement, that is (A) ⊕ B)) . The important truth values to compare are in columns 2 and 6 (circled), because that is the truth values of individual propositions A) and B)

As we mentioned earlier, The rule for [⊕]

**is that produces a value of****true**__if__

**one but not both of its operands is true**

__.__*We now have all the possible truth values for the overall proposition A) or else B).*

The table is now complete and irrefutable according to our own rules, all we have to do is look for the result.

The table is now complete and irrefutable according to our own rules, all we have to do is look for the result.

**Starting condition is that there is a queen in the hand. Or in other words, there is p)****Here I have circled in the table in which cases p) is true.**

**And then we can see that there is only one case in the table where the overall statement (A**⊕**B) is true, and that p) is also true, which is the**__second line__.So....

....

....

**What follows? if we look at "q" on this line ?**

Conclusion :

**In the case when p is true, and the overall statement is true and the main operator is an exclusive disjunction, q is false.**

It's counter intuitive, but there it is.

It's counter intuitive, but there it is.

*The answer is ~q or “*

**no ace.**”------------------

I have shown my work, I can discuss it if you like. I actually think I can see how the reasoning works now that I've done the demonstration, and can even describe it in non formal logic terms, but it still sounds fucked and counter intuitive when I try.

PS : here is an article, specific problem is around page 204

file:///tmp/mozilla_kora0/10.1.1.333.6706_1.pdf