How do I normalize and simplify (A ^ B) --> !B v C v !(A v C)
我如何规范化和简化(^ B)——> ! B v C v !(v C)
I've normalized the expression using the rule that (A->B) = !A or B. But I'm not sure how to simplify it. I've ended up with the answer !A v !B v C.
我用(A->B) = !A或B的规则对表达式进行了规范化，但我不知道如何简化它。我得到了答案，A v B v C。
Is this correct and if not, where am I going wrong?
这是正确的吗?如果不是，我哪里出错了?
1 个解决方案
#1
0
I'm getting the same answer as you.
我得到的答案和你一样。
1. (A ^ B) => !B V C V !(A v C)
2. (A ^ B) => !B V C V (!A ^ !C)
3. (A ^ B) => !B V (C V (!A ^ !C)) //(C V (!A ^ !C)) => C V !A
4. (A ^ B) => !B V (C V !A)
5. (A ^ B) => !A V !B V C
6. !(A ^ B) V (!A V !B V C)
7. (!A V !B) V (!A V !B V C)
8. !A V !B V C
Suggestion...Do a truth table for the expression in step 1 and see if it matches the truth table for the expression in step 8. That will verify that our logic is correct. As far as simplification goes, step 8 is as far as it can go.
建议……为步骤1中的表达式做一个真值表，看看它是否与步骤8中表达式的真值表相匹配。这将验证我们的逻辑是否正确。就简化而言，第8步是它所能做到的。
Hope this helps!
希望这可以帮助!
#1
0
I'm getting the same answer as you.
我得到的答案和你一样。
1. (A ^ B) => !B V C V !(A v C)
2. (A ^ B) => !B V C V (!A ^ !C)
3. (A ^ B) => !B V (C V (!A ^ !C)) //(C V (!A ^ !C)) => C V !A
4. (A ^ B) => !B V (C V !A)
5. (A ^ B) => !A V !B V C
6. !(A ^ B) V (!A V !B V C)
7. (!A V !B) V (!A V !B V C)
8. !A V !B V C
Suggestion...Do a truth table for the expression in step 1 and see if it matches the truth table for the expression in step 8. That will verify that our logic is correct. As far as simplification goes, step 8 is as far as it can go.
建议……为步骤1中的表达式做一个真值表，看看它是否与步骤8中表达式的真值表相匹配。这将验证我们的逻辑是否正确。就简化而言，第8步是它所能做到的。
Hope this helps!
希望这可以帮助!