Consider the statement, “If Tommy doesn’t eat his broccoli, then he will not get any ice cream.” Which of the following statements mean the same thing (i.e., will be true in the same situations)? Select all that apply.
Suppose that your shady uncle offers you the following deal: If you loan him your car, then he will bring you tacos. In which of the following situations would it be fair to say that your uncle is a liar (i.e., that his statement was false)? Select all that apply.
Consider the sentence, “If \(x \ge 10\text{,}\) then \(x^2 \ge 25\text{.}\)” This sentence becomes a statement when we replace \(x\) by a value, or “capture” the \(x\) in the scope of a quantifier. Which of the following claims are true (select all that apply)?
Consider the statement, “If I see a movie, then I eat popcorn” (which happens to be true). Based solely on your intuition of English, which of the following statements mean the same thing? Select all that apply.
This is not equivalent to the original statement. Maybe I also eat popcorn when I watch TV? In that case, the original statement would be true, but this one would be false.
If I don’t eat popcorn, then I don’t see a movie.
Correct.
It is necessary that I eat popcorn when I see a movie.
This is equivalent to the original statement (although here “necessary” is used in a logical sense).
To see a movie, it is sufficient for me to eat popcorn.
Just because I eat popcorn, doesn’t mean I see a movie. I might eat popcorn in other situations. So this is not equivalent to the original statement.
I only watch a movie if I eat popcorn.
Another way of saying this is, “I watch a movie only if I eat popcorn.” This is equivalent to the original statement.
