>>>So, what are your predictions?
>>>
>>>

? .f. or .t. or .f. and .f. or .f.
>>>? .f. or .f. or .t. and .f. or .f.

>>
>>True and False
>
>We reasoned from left to right.
>
>Our initial reasoning for the 1st one was:
>step 1) false or true = true
>step 2) true or false = true
>step 3) true and false = false
>step 4) false or false = FALSE
>
>Our initial reasoning for the 2nd one was:
>step 1) false or false = false
>step 2) false or true = true
>step 3) true and false = false
>step 4) false or false = FALSE
>
>We now know we were wrong and why. But does anybody here (except Sergey, who obviously appears to know why) know why?

The precedence of AND means that AND is evaluated first (like multiplication) and then the OR (like addition). So your expressions basically read as

? .f. or .t. or (.f. and .f.) or .f.
? .f. or .f. or (.t. and .f.) or .f.

The precedence of conjunction over disjunction makes parentheses unnecessary, hence they need not be written. It always behaves as if they are.