The truth value of a logical expression is defined recursively as:

The truth value of t is t.

The truth value of f is f.

The truth value of (x1 x2) is t if both x1 and x2 have truth value t, it is f otherwise.

The truth value of (x1 x2) is f if both x1 and x2 have truth value f, it is t otherwise.

The truth value of (x) is f if x has truth value t, it is t otherwise.

Define a CFG that generates the following language over{t, f,,,,(,),=}:

L={w=x: w is a logical expression over{t, f},x{t, f}, and x is the truth value of w}

Thus, t = t, ((t f) f) = f, and (((t f) f)) = t are in L, but ((t f) f) = tand (t f) f = f are not: the former because ((t f) f) is false and not true, the latter because the expression lacks the outermost set of parentheses.