Use rules of logic/ inference to prove the following argument. List each rule and proposition used for each step. Note: you will need to derive more statements than listed. 1) ¬(p → q)                 2) p ∨r                          ∴ ¬r ∨¬q

Instructions: For each argument below, evaluate the truth of each premise (write “true,”“false,” or “questionable”). Then evaluate the argument’s support (write “valid” or“invalid,” and briefly explain why). Finally, determine the overall quality of theargument (write “sound” or “unsound”), and briefly explain whySAMPLE: P1) Some dads have a beard.P2) All bearded people are mean.C) Some dads are mean.Truth of premise 1: trueTruth of premise 2: questionable (“mean” is subjective)(true, false, or questionable)Support: valid(valid or invalid)Why: the premises establish that bearded dads are mean,so some dads (the ones with beards) are meanOverall: unsound(sound or unsound)Why: fails the truth test -- premise 2 is not true1. P1) All cats are fish.P2) All fish live underwater. .C) All cats live underwater.Truth of premise 1:Truth of premise 2:(true, false, or questionable)Support:(valid or invalid)Why:Overall:(sound or unsound)Why:   1. P1) All cats are fish.P2) All fish live…

Determine whether the argument is valid or invalid.          r ↔ p         q ∨ r     ∴  p ∨ r

p = I am tired q = Class is early If I am tired then class is early. This is an early class. Therefore, I am tired. Write the argument using logic symbols, then show if the argument is valid or invalid.