This puzzle is an homage to Brian Tivol’s 2002 Hunt puzzle True and False.
Your goal here is to make the statements logically consistent: if a statement is marked as true, the thing it says should actually be true, and if the statement is marked as false, the thing it says should actually be false.
There are two logically consistent solutions, one where the top left statement is true, and one where the bottom right statement is true. Whether or not you consider Y to be a vowel, there are still only the same two logically consistent solutions.
The only consistent solution where the top left statement is true is:
Reading across the rows in 5 bit encoding (the way that the top left statement tells you to), you get RIGHT.
The only consistent solution where the bottom right statement is true is:
Reading down the columns in 5 bit encoding (the way that the bottom right statement tells you to), you get ANGLE.
The final answer to this puzzle is RIGHT ANGLE.