Decide whether the argument is valid or a fallacy, and give the form that applies.

If the fire alarm rings, then you will leave the building.

If you leave the building, then you'll be safe.

If the fire alarm rings, then you'll be safe.

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Part 1

Let p be the statement

"the fire alarm rings,"

q be the statement

"leave the building,"

and r be the statement

"you'll be safe."

The argument is

a fallacy

valid

by

left bracket left parenthesis p right arrow q right parenthesis logical and tilde p right bracket right arrow tilde q ,

left bracket left parenthesis p right arrow q right parenthesis logical and left parenthesis q right arrow r right parenthesis right bracket right arrow left parenthesis p right arrow r right parenthesis ,

left bracket left parenthesis p right arrow q right parenthesis logical and p right bracket right arrow q ,

left bracket left parenthesis p logical or q right parenthesis logical and tilde p right bracket right arrow q ,

left bracket left parenthesis p right arrow q right parenthesis logical and tilde q right bracket right arrow tilde p ,

left bracket left parenthesis p right arrow q right parenthesis logical and q right bracket right arrow p ,

or

modus tollens.

reasoning by transitivity.

fallacy of the inverse.

fallacy of the converse.

disjunctive syllogism.

modus ponens.