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booleanboolean-logicboolean-expression

Rewrite Boolean Expression without Parentheses

I have a black box processing system that accepts boolean expressions but does not support parentheses. I want to input a boolean expression like this:

A && (B || C)

However, when I input it as:

A && B || C

it evaluates expressions as if I had entered:

(A && B) || C

Is there any way to rewrite my expression to get the desired behavior of A && (B || C) without parentheses? Thanks!

Solution

  • There's a relation between precedence but, you can use associative and distributive laws to resolve this.

    A && B || A && C

    Truth tables match.

    Be careful when implementing this. Not all compilers and languages use the same precedence and evaluation order.