Greetings, Off-Topic. On this particular occasion, I have decided to have an entertaining discussion with all of you by composing a simple game based on logical-reasoning.
Firstly, while utilizing mathematics, we have objective statements such as "x = 5"
Those particular type of statements are properly known as "predicates", given that they equate to either the Boolean values of true and/or false. within the above premise, it merely defines the quantity that variable 'x' represents.
Therefore, it is "true" predicate.
Although I used "x = 5", we could use symbolic notation such as this:
E(x) = 5
Where uppercase "E" refers to the word "Equal", and the input variable 'x' receives the quantity described on the opposite side of the "=" operand.
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Recognizing the above objective explanation, the goal of the game is rather basic: to derive logical expressions to be interpreted by other users.
I have devised a minimal list of logical symbols below:
"-->" - The logical "if-then" operator. "If certain cookies are delicious, then some grapes are bluish"(Note that the premise predicate and the conclusion predicate do not necessarily need to be related. They merely need to have an obtainable Boolean value.
'~' - The logical "NOT" operator. It merely negates "true"/"false" Boolean predicates into the opposite Boolean value.
~"I decided to traverse the area" becomes "I decided not to traverse the area."
"^" - The logical AND operator. "(1+1 = 2) ^ (2 + 2 = 4) --> (5 + 5) == 10", which is true, given that "1 + 1 = 2 ^ 2 + 2 = 4" are both (true ^ true) respectively.
Disregarding all of the other logical operators for the current moment, this is a sample expression that I have devised below:
Suppose that we have variables 'a' and 'b':
a = 100
b = 50
Firstly, let us define a predicate to determine whether the first value is a factor of the second value:
R(a,b) = (a % b)
This will retrieve the remainder of the division operation "a/b", using the difference between 'a' and 'b' as a referent.
Likewise, R(b,a) would also retrieve the remainder of the division operation "b/a", using the difference between 'b' and 'a' as a referent.
If I had an expression such as this:
(R(a,b) = 0) ^ (R(b,a) = 0)
It would be an expected case of a true/false pair. This is due to the mere fact that the (100 % 50) does not have a remainder, whereas (50/100) does indeed have a remainder of fifty itself.
Hopefully the above descriptions provides a rather wholesome and otherwise precise discussion involving mathematical logic. |