Consider the following arguments. If the argument is valid, identify the rule of inference.

Otherwise, state whether the converse or the inverse error is made. $($Hint: Use symbols to

write the logic form of each argument.$)$

$(1)n$ is divisible by $2$ or $n+3$ is odd.

$n$ is not divisible by $2.$

:$.n+3$ is odd.

$(2)$ If I allocate enough time to prepare for the final, then I will do well on the final.

I do perform well on the final.

:$.$ I have allocated enough time to prepare for the final.

$(3)$ If I get a passing grade for this class, then I will graduate in May.

I do get a passing grade for this class.

:$.$ I will graduate in May.

$(4)$ John is a cybersecurity major.

John likes mathematics.

:$.$ John is a cybersecurity major who likes mathematics.