What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: If it is overcast, then it is cold. If it is cold, then it is overcast. Patricia is listening to a song if and only if it is cold. For all y, y will not listen to a song.
It is overcast if and only if it is cold can be inferred via the biconditional introduction rule. It is cold if and only if it is overcast can be inferred via the biconditional introduction rule. If Patricia listens to a song, then it is cold can be inferred via the biconditional elimination rule. If it is cold, then Patricia is listening to a song can be inferred via the biconditional elimination rule.