Strugggling to understand this logical reasoning

[bushra1175]

I don't understand how step 3 was derived using the law of contrapositive. The law applies to p and q in the inference rules above so I don't understand how it was used on r and s. I would really appreciate your help on this.

 

[lex]

Please see attached.

 

[Dr.Peterson]

View attachment 25327
View attachment 25328
View attachment 25329

I don't understand how step 3 was derived using the law of contrapositive. The law applies to p and q in the inference rules above so I don't understand how it was used on r and s. I would really appreciate your help on this.

Step 3 is derived from H₂ by taking the contrapositive. It would be nice if the format allowed them to say that.

Surely you aren't saying that you think rules can't be applied unless the letters are the same. You can't get past the first page of a chapter on logic without understanding that letters in rules are placeholders for anything.

 

[JeffM]

We are accepting that [MATH]r \implies \neg s.[/MATH]
[MATH]\therefore \text { By the law of contrapositive, } ( \neg ( \neg s) \implies \neg r) \implies (s \implies \neg r).[/MATH]