Don't get too bogged-down in the abstract...
In real-world programs, the variables represent the state of something "real", like : IF (a blank CD is inserted) AND (the user clicks "burn")...
Bitwise manipulation is similar, in that each bit usually represents the state of something. (There are exceptions, such as XOR encryption.)
Most of the time, you won't see the words "true" or "false", or the numbers "1" or "0".
This is how computer programs "make decisions" with if-statements. Every decision/choice only has only two outcomes... True/False (yes/no).
In many real situations, there is more than one possibility. Typically, you have to continue through a series of true/false questions/decisions 'till you find a true result, or until you find the right combination of true results.
Once you start to understand how Boolean logic is used in "real programs"... perhaps after you've written a couple of programs or studied a few examples... you should go-back and make sure you understand the abstract concepts & notation.
