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Placement Test Practice — Set Theory & Logic
Placement Test Practice — Set Theory & Logic
Practice Test — 20 Questions
1. $A = \{1,2,3\}$, $B = \{2,3,4\}$. $A \cap B = $?
2. $|A \cup B|$ if $|A|=10$, $|B|=7$, $|A \cap B|=3$?
3. Negate: $\forall x\, P(x)$.
4. Truth value: $T \to F$?
5. Is $p \lor \lnot p$ a tautology?
6. $(A \cup B)' = $?
7. Contrapositive of "if it rains, the ground is wet"?
8. $A - B$ when $A \subseteq B$?
9. How many elements in $\mathcal{P}(\{1,2,3\})$?
10. Is $\{\emptyset\} = \emptyset$?
11. $p \land q$ is true only when?
12. Negate: $\exists x\,(x^2 = 4)$.
13. Base case of induction for $n \geq 1$?
14. Direct proof: product of two odd numbers is odd.
15. What is a counterexample?
16. $A \cup A' = $?
17. $p \to q$ is equivalent to?
18. How many rows in a truth table with 4 variables?
19. What does QED or ∎ mean?
20. Negate: "No student failed."
Show Answer Key
1. $\{2,3\}$
2. $14$
3. $\exists x\, \lnot P(x)$
4. False
5. Yes
6. $A' \cap B'$
7. "If the ground is not wet, it did not rain."
8. $\emptyset$
9. $2^3 = 8$
10. No — $\{\emptyset\}$ has one element
11. Both $p$ and $q$ are true
12. $\forall x\,(x^2 \neq 4)$
13. $n = 1$
14. $(2a+1)(2b+1) = 4ab+2a+2b+1 = 2(2ab+a+b)+1$, odd ∎
15. A specific case that disproves a universal statement
16. $U$ (the universal set)
17. $\lnot p \lor q$
18. $16$
19. "Which was to be demonstrated" — marks end of proof
20. "Some student failed."