!(1 || 0) ANSWER 0.

Logical operators are usually used to apply on the result of the two or more conditional statements that returns either true or false.
like if((a>b) ||(a>c)).

Any non zero value for these operators will be considered as "true" (includes negative numbers also) and zero value will be considered as "false".

value for the true is "1"
value for the false is "0"

1 || 1 = 1
1 || 0 = 1
0 || 1 = 1
0 || 0 = 1

!(1) = 0
!(0) = 1

first (1||0) will be computed the output will be 1 based on the above table

!(1) will be computed the result of which will be 0

Remeber any non zero value will be "true" and zero value will be false for the logical operators.

Hope it has cleared your doubt.