Logic
A proposition is a statement with one of these two values.
What are True and False?
If we want to use a direct proof to prove "If P, then Q", what do I assume/suppose in the first line of my proof.
What is "Suppose P"?
For any given set, A, both itself and this set are guaranteed to be subsets of A.
What is the empty set?
A graph consists of edges that connect vertices, also known by this "n"ame.
What are nodes?
A relation R on a set A is an equivalence relation if it is...
What is "symmetric, transitive, and reflexive?"
This operator only outputs True if both inputs are true.
What is conjunction? (Acceptable: AND)
If I want to prove the statement: "If P, then Q" and I start out supposing "Not Q" and use theorems/definitions/math to show "Not P," what proof technique did I use?
What is a "Contrapositive Proof"?
Set operations can be represented by algebra, membership tables, or this diagram that uses intersecting circles.
What is a Venn Diagram?
The number of edges in the tree from the root to the deepest node
What is the "height of a tree"?
This property states if xRy, then yRx.
What is "symmetry"?
It's the only unary logic operator, meaning it takes one input statement rather than two.
What is negation? (Acceptable: NOT)
Suppose I am proving the proposition: "If a2 is even , then a is even." If I want to do a proof by contradiction what should I suppose?
What is: "a2 is even and a is not even"?
This "product" of A and B is defined as the set of ordered pairs (x,y), where x is in A and y is in B.
What is the Cartesian Product?
The three elements in the ordered triple that define a graph.
What are the "set of nodes (N), set of edges/arcs (A), and function (g)"?
Suppose R is an equivalence relation on a set A. Given any element a ∈ A, this is the set for the equivalence class [a].
The implication A-->B is equivalent to A' __ B, with the blank being this operator.
What is Disjunction? (Acceptable: OR)
When I am trying to prove that the statements S1, S2, … are all true and I assume that Sk is true.
What is the inductive hypothesis?
It's the cardinality of the power set of {a,b,c,d}
What is 16?
An edge/arc that connects a node back to itself.
What is a "loop"?
Among the defining properties of equivalence relations, this is the one which states if aRb and bRc, then aRc.
What is transitive?
This rule, states if "P" and "P -> Q", then "Q".
What is Modus Ponens?
The basis step if I am trying to prove: "If n \in N, then 1+3+5+7+...+(2n-1)=n2".
What is "Plug in n = 1 and show 1 = 12"?
The intersection of the set A={1, 2, 3} and B = {1, 2, 3, 4}.
What is "A"?
A tree where each node has at most two children.
What is a binary tree?
The set {{a,c}, {b}, {d}} is a partition of this set.
What is "A = {a, b, c, d}"?