How to find formula F with statement variables from truth table (propositional logic)?

2013-09-08 4:53 pm
Hey guys i'm stuck at one task, i need a bit help with a small explanation, please

Task:

Find a formula F with statement variables H, M and B so that the truth value table for F looks
as follows:

H M B | F
1 1 1 | 1
1 1 0 | 1
1 0 1 | 1
1 0 0 | 0
0 1 1 | 1
0 1 0 | 0
0 0 1 | 0
0 0 0 | 0

1 = True 0 = False

Thanks alot!

回答 (1)

2013-09-08 7:32 pm
✔ 最佳答案
Consider two sets.

1 1 1 ⇒ 1
1 1 0 ⇒ 1
1 0 1 ⇒ 1
0 1 1 ⇒ 1

1 0 0 ⇒ 0
0 1 0 ⇒ 0
0 0 1 ⇒ 0
0 0 0 ⇒ 0

These two sets imply that
The formula is true if and only if
There are at least two true variables. Therefore,
F ⇔ (H ∧ M) ∨ (H ∧ B) ∨ (B ∧ M)
F ⇔ (H ∧ (M ∨ B)) ∨ (B ∧ M).


收錄日期: 2021-05-01 14:55:59
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20130908085321AARAHjt

檢視 Wayback Machine 備份