Set theory

Question 1

What is a complement of a set

Answer 1

All the items not in the set A, in the global set

Question 2

What are De-morgans’ Laws

Answer 2

not(A unison B) = Not(A) intersection Not(B)

not(A Intersection B) = Not(A) unison Not(B)

Question 3

What is the definition of a partition

Answer 3

a partition is a collection of sets that
are “mutually exclusive and collectively exhaustive”.

Question 4

What is the Cardinallity of a set?

Answer 4

For a set A, the cardinality of A is the number of items in the set A

Question 5

What is the Inclusion exclusion principle?

Answer 5

If A and B are sets of finite cardinality

|𝐴 ∪ 𝐵| = |𝐴| + |B| - |𝐴 ∩ 𝐵|.

Question 6

What is the product principle of counting

Answer 6

states that when 𝐴1, 𝐴2, … , 𝐴𝑛 are finite sets, then the cardinality of their Cartesian product is equal to the product of their
individual cardinalities:

Question 7

The unordered sequence of 𝑘 elements, selected without replacement, from a set with 𝑛 elements is called a combination. The number of possible combinations, 𝐶(𝑛, 𝑘)
is given by:

Answer 7

𝐶(𝑛,𝑘) = (𝑛) = 𝑛! / 𝑘 (𝑛 − 𝑘)!𝑘!

n and k are referred to as the binomial coefficients

Question 8

What is the number of possible outcomes in ordered sampling with replacement

Answer 8

n^k

k = number of items removed
n = set cardinallity

Question 9

what is the number of possible outcomes in ordered sampling without replacement, when order does not matter

Answer 9

n choose k