What does the statement a is true for x and b is true for y mean ? does it mean x can equals b and also ?
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What does the statement a is true for x and b is true for y mean ? does it mean x can equals b and also ?
Answers
There is no transitive property implied in your given logic. I'm not even sure what it is trying to say.
Let's take a concrete example:
a = "The number is divisible by 2"
x = Even numbers
b = "The number is not divisible by 2"
y = Odd numbers
The statement a ("divisible by 2") is true for set x (the even numbers)
The statement b ("not divisible by 2") is true for the set y (the odd numbers)
So there is nothing that relates the set x (even numbers) and the statement b ("not divisible by 2")
Without some idea of what a, b, x, and y are, the statements are meaningless.
"a is true for x" suggests that "a" is a logical or arithmetic expression of some sort that can be true or false, and that "x" is a condition or set of conditions that can be applied to "a" so that the value of "a" can be determined. This suggestion is merely that, a suggestion or an expectation. It has no basis in the information actually provided.
Assuming the above holds for "a is true for x" and again for "b is true for y", absolutely nothing is implied about the relationship between "a" and "b", "x" and "y", "a" and "y", or "b" and "x".
Even going this far is reading a lot into a basically meaningless statement, attempting to give some tiny shred of meaning where none actually exists.