Lessons · Quantitative Reasoning
CLT Quantitative Reasoning · Lesson
Logic
Logic questions test what must follow from given statements. "If P, then Q" guarantees its contrapositive, "If not Q, then not P," and nothing else.
- Write each statement as an arrow: P → Q.
- The contrapositive (not Q → not P) is always true when the statement is.
- The converse (Q → P) and inverse (not P → not Q) are not guaranteed.
- For "some," "all" and "none" statements, draw a quick circle diagram.
Q. "If it rains, the game is canceled." Which must be true?
Answer If the game was not canceled, it did not rain.
That is the contrapositive. "If the game was canceled, it rained" is the converse; the game might be canceled for another reason.
- Choosing the converse because it sounds natural.
- Reading "only if" as "if." "P only if Q" means P → Q.
Every practice question comes with a full explanation, including why each wrong choice is wrong. Free, with no account.