The thing you need to focus on here first is the properties of prefix and postfix operators and their differences.
For Postfix increment and decrement operators, C11, chapter §6.5.2.4, (emphasis mine)
The result of the postfix ++ operator is the value of the operand. As a side effect, the
value of the operand object is incremented [...] The postfix -- operator is analogous to the postfix ++ operator, except that the value of
the operand is decremented.
For Prefix increment and decrement operators, C11, chapter §6.5.3.1, (emphasis mine)
The value of the operand of the prefix ++ operator is incremented. The result is the new
value of the operand after incrementation. [...] The prefix -- operator is analogous to the prefix ++ operator, except that the value of the
operand is decremented.
Now, there comes the property of the Logical AND (&&) operator. From chapter §6.5.13, (again, emphasis mine)
the && operator guarantees left-to-right evaluation;
if the second operand is evaluated, there is a sequence point between the evaluations of
the first and second operands. If the first operand compares equal to 0, the second
operand is not evaluated. [...]
So, in your case,
int a = 1, b = 1, c = -1;
c = --a && b++;
gets evaluated as
c = 0 && .....; // done..., a is decremented to 0,
// so, LHS of && is 0, RHS is not evaluated,
// b remains 1
// and finally, C gets 0.
On the other hand, if logical OR (||) would have been used, then, as per the property, mentioned in chapter §6.5.14
[...] the || operator guarantees left-to-right evaluation; if the
second operand is evaluated, there is a sequence point between the evaluations of the first
and second operands. If the first operand compares unequal to 0, the second operand is
not evaluated.
So, for the case
int a = 1, b = 1, c = -1;
c = --a || b++;
it will be evaluated as
c = 0 || 1; //yes, b's value will be used, and then incremented.
So,
printf("%d %d %d", a, b, c);
will be
0 2 1