SRL Archive - Mathematics

I'm am completely stuck with this question in my homework.

Use resolution to show the hypotheses “Allen is a bad boy or Hillary is a good girl” and
“Allen is a good boy or David is happy” imply the conclusion “Hillary is a good girl or
David is happy.”

Can anyone point me in the right direction?

"Allen is a bad boy or Hillary is a good girl" can be represented as (not a) or b
"Hillary is a good girl or David is happy" can then be represented as a or c
If you assume a is true then b must be true. If you assume a is false then c must be true. So either b or c is true.

Edit: woah just read this. Hint, don't logic while playing league.

Helps to look at it in a table if you're stuck.

[table="width: 1000, align: center, class: grid"]
[tr]
[td]Given: [/td]
[td][/td]
[td]Allen is bad[/td]
[td]OR[/td]
[td]Hillary is good[/td]
[td][/td]
[td]AND[/td]
[td][/td]
[td]Allen is good[/td]
[td]OR[/td]
[td]David is happy[/td]
[td][/td]
[td]IMPLIES[/td]
[td][/td]
[td]Hillary is good[/td]
[td]OR[/td]
[td]David is happy[/td]
[td][/td]
[/tr]
[tr]
[td]Inference:[/td]
[td]([/td]
[td]¬ A[/td]
[td]\/[/td]
[td]H[/td]
[td])[/td]
[td]/\[/td]
[td]([/td]
[td]A[/td]
[td]\/[/td]
[td]D[/td]
[td])[/td]
[td]->[/td]
[td]([/td]
[td]H[/td]
[td]\/[/td]
[td]D[/td]
[td])[/td]
[/tr]
[/table]

And you can then maybe simplify the expression from there and figure out what makes the expression true..

Work backwards from the conclusion;
"Hillary is a good girl or David is happy.”
If we assume Hillary is a good girl then we know Allen is not a bad boy (implied good boy) because “Allen is a bad boy or Hillary is a good girl”.
Now that we know Allen is an (implied) good boy we know David is (implied) unhappy because “Allen is a good boy or David is happy”.

Therefore the conclusion "Hillary is a good girl or David is happy.” is sound.

Referring to Allen is bad as A':

The thing boils down to A'+H and A+D. Treating everything(A,H,D) as non-empty sets/regions it's pretty easy to draw out the venn diagram and see that this is true on all the regions remaining (of course this method won't scale, but it could be helpful for building intuition about this stuff)

Brandon nailed it. of course, you'll have to state that A represents Allan being good and H represents Hilary being good etc etc.

Propably OP has done his homework already, but I was just curious if I can solve it with boolean algebra…

but whuh, those 2 expressions are not equal:

From: bg5
Propably OP has done his homework already, but I was just curious if I can solve it with boolean algebra…

but whuh, those 2 expressions are not equal:

just means when the result is evaluated true, gives the hypothesis, so there would be 2 non equal as this is not assumed to be in the hypothesis