Logical test question


As much as I do recall, the question went like this:


Referring to the above information, if “AND” means a compound statement is true only if both statements are true, and “OR” is a compound statement if either is true, which of the following statements must be true?

  1. (A OR B) OR C
  2. (A AND B) OR C
  3. (A AND B) AND C
  4. (A OR B) AND C
  5. A AND (B OR C)

My comment: I just can’t see the logic in this albeit it may appear to be dazzlingly simple and straight-forward to some. Would anyone please point out the solution and explain a little?
All I know is that if a statement is FALSE AND TRUE, the compound statement is inconclusive. Right?


No. Here it goes:

  1. First we solve A OR B, we get TRUE. Then we take this new conclusion and use the function OR with C. So TRUE Or FALSE again gives us TRUE. So, 1 is true.

  2. A AND B is false as both of them are not TRUE. And FALSE or FALSE is also FALSE. So, 2 is False.

  3. is simply FALSE following the logic of 2 and using AND.

  4. Solve it A OR B, it gives us TRUE. But TRUE AND C, gives us FALSE as both are not TRUE. So, 4 is FALSE.

  5. First solve it for B OR C, which gives us TRUE as one of them is TRUE. But A AND TRUE, gives us a FALSE result as both of them are not TRUE. So, 5 is FALSE.

Hence only Statement 1 is TRUE. I guess you faced this question in a Technical scheme test as the solution is very common to anyone studying computers or physics but can be confusing for everyone else.

General rule is that first solve the brackets, ask yourself a question is the operation AND or OR. If it is AND, both conditions need to be true to get a TRUE result. In the case of OR, only one of either statements needs to be TRUE to get a TRUE result.

I just saw the date and probably you won’t need it now but I will leave it for anyone else.