Hi everyone!
I hope all of you guys have had a nice week so far, today I'd like to write a short post on what we learned in class recently!
Today I'd like to talk about this nifty thing we learned in class called vacuous truth. Sounds complicated or abstract at first right? How can a truth be empty? Vacuous truth is this interesting concept that in an implication, where A implies B, if A is never True, then you can never say that A doesn't imply B!
Let's first look at a 'real-life' example:
If a person were to say, "If your apple turns into a banana when submerged under water, then the apple must have grown upside down in the ancient tombs of the ancient Egyptian Pharaohs," you would have no means of proving that person wrong, since you would first have to find an apple that turned into a banana when submerged under water!
Therefore what this person has said is vacuously true.
Now let's look at an example dealing a little more with math:
The statement, "if x/0 = 2, then x must be a prime number," is also vacuously true because x/0 will never be 2, since it is undefined.
As a closing example, I just wanted to show that it doesn't matter what goes in the predicate of the statement, as long as the antecedent never comes true, then the statement remains vacuously true.
The statement is, "if the abs(x + y + 1) = -2, then Kobe Bryant and Shakespeare will ride off into the sunset on a hippo and a sponge." Sounds ridiculous, doesn't it? Nonetheless, this statement cannot be wrong as long as the derivative of x^4 is never 2. Who knows? Maybe one day if people are able to prove that the absolute value of 3 numbers can be negative, we'd be able to see such a wondrous sight.
Anywho, thanks for reading this week's post!
Lana :)
I hope all of you guys have had a nice week so far, today I'd like to write a short post on what we learned in class recently!
Today I'd like to talk about this nifty thing we learned in class called vacuous truth. Sounds complicated or abstract at first right? How can a truth be empty? Vacuous truth is this interesting concept that in an implication, where A implies B, if A is never True, then you can never say that A doesn't imply B!
Let's first look at a 'real-life' example:
If a person were to say, "If your apple turns into a banana when submerged under water, then the apple must have grown upside down in the ancient tombs of the ancient Egyptian Pharaohs," you would have no means of proving that person wrong, since you would first have to find an apple that turned into a banana when submerged under water!
Therefore what this person has said is vacuously true.
Now let's look at an example dealing a little more with math:
The statement, "if x/0 = 2, then x must be a prime number," is also vacuously true because x/0 will never be 2, since it is undefined.
As a closing example, I just wanted to show that it doesn't matter what goes in the predicate of the statement, as long as the antecedent never comes true, then the statement remains vacuously true.
The statement is, "if the abs(x + y + 1) = -2, then Kobe Bryant and Shakespeare will ride off into the sunset on a hippo and a sponge." Sounds ridiculous, doesn't it? Nonetheless, this statement cannot be wrong as long as the derivative of x^4 is never 2. Who knows? Maybe one day if people are able to prove that the absolute value of 3 numbers can be negative, we'd be able to see such a wondrous sight.
Anywho, thanks for reading this week's post!
Lana :)
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