Mathematics from zero
Logic and sets: multiple-choice review
Six questions that cut across the whole unit. None of them ask for a definition — each one asks you to apply a rule: read a truth value, evaluate a combination, or combine two sets and check the result.
Confirm you can tell a statement from a non-statement, apply the AND, OR, and NOT rules to work out a combined truth value, and combine two sets correctly by union and intersection.
Which one of these sentences is a statement in the logical sense?
A friend says '2 + 2 = 5 cannot be a statement, because it is false.' Are they right?
Using the facts '6 > 1' is true and '3 > 7' is false, what is the truth value of (6 > 1) AND (3 > 7)?
In ordinary logic, when is a statement joined by OR false?
A is the set {1, 2, 3} and B is the set {3, 4, 5}. What is their intersection?
A is {2, 4, 6} and B is {4, 6, 8, 10}. What is the size of their union?
The through-line of this unit is one idea applied three ways. A statement carries a fixed truth value, true (1) or false (0); a question, command, or opinion does not. AND, OR, and NOT take those truth values and produce a new one — AND needs both true, OR needs at least one true, NOT flips. Sets answer a yes-or-no membership question, and combine the same way the connectives do: union is the generous “or”, intersection is the strict “and”.