Proof Techniques flashcards
13 practice cards drawn from the Proof Techniques lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.
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What does a direct proof never do?
assume the conclusion
from “Direct Proof”
A direct proof of "if n is odd then is odd" starts how?
by writing n = 2k + 1
from “Direct Proof”
After proving the contrapositive, what remains to be done?
nothing
from “Proof by the Contrapositive”
Which claim is the contrapositive route best suited to?
if x + y is odd, then x and y differ in parity
from “Proof by the Contrapositive”
A claim about n mod 3 is split into n = 3k and n = 3k + 1. What is wrong?
the case n = 3k + 2 is missing
from “Proof by Exhaustion”
Both cases in a two-case proof reach the conclusion. What follows?
the claim holds in every case
from “Proof by Exhaustion”
Which one counterexample disproves the claim drawn?
1
from “Disproof by Counterexample”
Put 8 objects into 3 boxes. What is the largest number some box must hold?
3
from “The Pigeonhole Principle”
A drawer holds socks in 6 colors, mixed up in the dark. How many must you take to be sure of a matching pair?
7
from “The Pigeonhole Principle”
How is "there is a whole number whose square is 49" proved?
by naming one such number
from “Proving Existence and Uniqueness”
What does the phrase "there exists a unique n" claim?
at least one n, and no more than one
from “Proving Existence and Uniqueness”
How many ways can 7 identical coins go into 4 labeled jars, empties allowed?
120
from “Counting by a Bijection”
How many ways can 7 identical coins go into 3 labeled jars, empties allowed?
36
from “Counting by a Bijection”