Is Reductio ad absurdum an umbrella term for all these rules of inference?

[brittle condor]

Studying rules of inference and noticed that reductio ad absurdum has multiple.
Is there a difference between a) and b)?

[solid radish]

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[balmy surge]

all these rules can be proven using the rule:
¬A -> false

     A

this is the ad absurdum reasoning

one thing to note:

¬A is defined as (A -> false)

hence, the rule

A -> false

    ¬A

is a tautology

[brittle condor]

-> is implication here?

[balmy surge]

hence, a.3 and b.2 do not follow from ab absurdum, you can prove them without

yes, -> is the implication

[brittle condor]

i was confused for a sec here but i understand now

thank you @balmy surge

[balmy surge]

you're welcome, don't forget to close the thread with +close if you're done

[brittle condor]

okie

+close

[neat turtle]

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[neat turtle]

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