Natural Deduction: Derive the conclusions of the following arguments using the rules of inference and the rules of replacement.

An unknown number of kids and buses are getting assigned. when assigning 4 kids to each bus, there are 2 kids that aren't placed in a bus. when assigning 8 kids to each bus, there are 2 empty buses. how many total kids are there?

Julia chooses a card at random from her set of cards. what is the probability that the card is labeled cat or hamster?

Which graph represents the solution set for the given system of inequalities? x+2y< 3 x+y> 4 3x-2y> 4