'If p → q then q → p?
I'm trying to get back into boolean algebra after many years without it, I'm currently working on an exercise that asks to verify if p → q or q → p are tautologies, p and q being very long expressions hard to simplify, yet p → q is very easy to prove a tautology using a truth table while q → p takes a lot longer to verify using a truth table.
Is the statement p → q ≡ q → p correct? I can't find concise info on this proposition but building the truth table makes it seem like it is correct.
If it is I could answer that since p → q is a tautology q → p is too.
Solution 1:[1]
When I understand your question right, then a look at the truth-table shows the following:
a -> b = c | b -> a = c
0 -> 0 = 1 | 0 -> 0 = 1
0 -> 1 = 1 | 0 -> 1 = 0
1 -> 0 = 0 | 1 -> 0 = 1
1 -> 1 = 1 | 1 -> 1 = 1
This show that a->b is not euqal to b->a.
I hope this help a little bit.
Sources
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Source: Stack Overflow
| Solution | Source |
|---|---|
| Solution 1 | Kretchen001 |