Before reading on to the main content of the section, complete this preview activity to start thinking about the types of questions this section will address.
Which of the following sentences should count as statements? That is, for which of the sentences below could you potentially claim the sentence was either true or false? Select all that apply.
You and your roommate are arguing, and they make the audacious claim that pineapple is good both on pizza and in smoothies. Which of the following are reasonable responses to this claim, from a logical point of view?
The claim that pineapple is good both on pizza and in smoothies is not claiming that it is only good at the same time. It is precisely claiming these two separate facts are both true.
The statement is half true because regardless of what you think about pineapple on pizza, we can all agree at least that pineapple is good in smoothies.
Your roommate now makes an even more outrageous claim: If a superhero movie is part of the Marvel Cinematic Universe, then it is good. Which of the following are reasonable responses to this claim, from a logical point of view?
This is false because there are good superhero movies, like Wonder Woman and Dark Knight, that are based on DC Comics, and so not part of the Marvel Cinematic Universe.
Your roommate just won’t let up with their outrageous claims. Now they claim that either every troll is a knave, or there is at least one troll that is a knight. What can you say to this?
Yes, this is true because every troll is either a knight or a knave. If it is not the case that all trolls are knaves, then there must be some troll that is a knight.
It’s true that if a troll said that all trolls are knaves they would have to be a knave and then it would be false that all trolls were knaves. But luckily there is another option.
