Logic
Proofs & Induction
Sets, Relations, Functions
Counting
Probability
100
The contrapositive of this conditional statement: 𝑝→¬𝑞.
What is 𝑞→¬𝑝 ?
100
We assume this in a direct proof of the statement: if 𝑥 is odd and 𝑦 is odd, then 𝑥+𝑦 is even.
What is "𝑥 is odd and 𝑦 is odd"?
100
This set operation:
What is 𝐴−𝐵 ?
100
This is the number of bit strings of length 15 that contain exactly five 1’s.
What is C(15,5)?
100
A coin is flipped 3 times. This is the probability that it lands on heads at least 2 times.
What is 1/2?
200
The truth value of this proposition: (¬𝑝∨𝑞)→𝑟 when 𝑝=𝑇, 𝑞=𝐹, and 𝑟=𝐹.
What is True?
200
We assume this in a proof by contrapositive of the statement: if 𝑥𝑦 is even, then 𝑥 is even or 𝑦 is even.
What is "𝑥 is odd and 𝑦 is odd"?
200
The class of this function:
What is Surjective?
200
This is the number of ways to permute the letters in the word “SUBSETS”.
What is ( 7! / 3! ) ?
200
A hand of 5 cards is drawn from a standard deck of 52 cards. This is the probability that it contains exactly one heart.
What is C(13,1)*C(39,4) / C(52,5) ?
300
The domain of 𝑥 that makes this quantified statement true: ∀𝑥(𝑥2=𝑥).
What is {0,1}?
300
The inductive hypothesis in a proof by induction of this statement: 𝑛!≥2n for 𝑛≥4.
What is 𝑘!≥2k for 𝑘≥4 ?
300
A function 𝑓:ℕ→ℕ defined by the rule 𝑓(𝑥)=𝑥+2 for all 𝑥∈ℕ is of this class.
What is Injective?
300
This the number of hands of 5 cards drawn from a standard deck of 52 cards that contain at least one heart.
What is C(52,5)−C(39,5) ?
300
This is the probability that a bit string of length 4 starts with a 1 or ends with a 0.
What is [2(23)-22]/24 ?
400
The negation of this quantified statement: ∀𝑥(𝑃(𝑥)∨¬𝑄(𝑥)).
What is ∃𝑥(¬𝑃(𝑥)∧𝑄(𝑥)) ?
400
We assume this in a proof by contradiction of the statement: if 𝑥𝑦 is even, then 𝑥 is even or 𝑦 is even.
What is "𝑥𝑦 is even and 𝑥 is odd and 𝑦 is odd"?
400
The property of this relation:
What is Anti-symmetric?
400
A cookie store sells 5 varieties of cookies. This is the number of ways to select 12 cookies if at least 3 must be chocolate chip.
What is C(13,9)?
400
A coin is flipped 3 times. This is the probability that it lands on tails at least 2 times given that the last flip lands on tails.
What is 3/4?
500
Given predicate 𝐿(𝑥,𝑦): “𝑥 loves 𝑦,” this logical expression states that "everybody loves somebody."
What is ∀𝑥∃𝑦𝐿(𝑥,𝑦) ?
500
The base cases in a proof by strong induction of this statement: any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.
What is 𝑛=8, 𝑛=9, and 𝑛=10 ?
500
The property of this relation:
1 0 0 0
0 1 0 0
0 0 0 1
1 0 0 1
What is Anti-symmetric?
500
This is the number of solutions for the equation 𝑥1+𝑥2+𝑥3+𝑥4=35 if 𝑥1, 𝑥2, 𝑥3, and 𝑥4 are nonnegative integers and 𝑥1≤3.
What is C(38,35)−(34,31)?
500
A die is biased so that rolling a 5 is twice as likely as rolling each of the other five numbers. This is the probability of rolling a number greater than 4 with this die.
What is 3/7?