Suppose there are 8 possible solutions to some problem. If we use a binary decision tree to represent an algorithm that solves the problem, what is the optimal depth?

Suppose there are 8 possible solutions to some problem. If we use a ternary decision tree to represent an algorithm that solves the problem, what is the optimal depth?

Suppose set S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and we define the following relation on S:

x ~ y iff x mod 4 = y mod 4

This relation is an equivalence relation because it is the kernel relation of the function f(x) = x mod 4. Fill in the equivalence class of 3, denoted by [3].

[0] = ???

[1] = {1, 5, 9}

[2] = ???

[3] = ???

If E and F are equivalence relations on set A, is E ∩ F an equivalence relation on A?

Which of the following are valid ways to show that a binary relation is an equivalence relation? Select all that apply.

Which of the choices below are valid partitions of set A? Select all that apply.

A = {0, 1, 2, 3, 4, 5, 6, 7}

Suppose set S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and we define the following relation on S:

x ~ y iff x mod 4 = y mod 4

This relation is an equivalence relation because it is the kernel relation of the function f(x) = x mod 4. Fill in the equivalence class of 0, denoted by [0].

[0] = ???

[1] = {1, 5, 9}

[2] = ???

[3] = ???

For a binary relation R on a set A, R is symmetric if...

Find the symmetric closure of the following relation over the set {a,b,c}:

{(a,b), (b,c)}

Find the transitive closure of the following relation over the set {a,b,c,d}:

{(a,b), (a,c), (b,c)}