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I used search and i did not find a hint for this. So now i have a logic equation which has unknown truth value X("problem is to solve the X from logic equation which has truth values False and True).

The equation is: T ∧ X ↔(if and only if) F ∧ X So i how start to solve X here? Let's say if i say X is False(i just presume it). Then T ∧ F ↔ F ∧ F . So here we have F ↔ F. And now it's True. So is it now solved? If i put True=X the we have False, cos F ↔ T = F. But am i supposed to have true here or should i keep doing something more? Of is there better way to find out X than just try False and True on X?

Reese Johnston
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Johnny
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1 Answers1

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When solving an algebraic equation (that is, one representing numbers, like $x + 3 = 6$) there are infinitely many possibilities to consider, so we can't just plug them in and check - it would be silly to try to solve $x + 3 = 6$ by checking $1 + 3$, $2 + 3$, $87 + 3$, $\pi + 3$, and so on, just waiting until we get $6$. So instead, we develop techniques (like subtracting from both sides of the equation, for example) for getting the answer without trying out all the possibilities. But the important thing to realize is that the reason we develop these techniques isn't because they're more "correct" than guess-and-check, they're just easier.

But with truth values, there are only two options, so trying out the options is easy - you demonstrated that for your "equation", $F$ works and $T$ doesn't. That makes $F$ the solution! Now, we could develop techniques like in algebra - indeed, "propositional calculus" could be considered the logic version of these algebraic techniques - but it would be overkill for a situation like this, like using a supercomputer to calculate $1+1$.

Reese Johnston
  • 17,988