If there are a large number of sequential members in a set, write as A={ 1,3,5,7, ...} (all odd numbers, to infinity). The **ellipses** (...) means continue the sequence. If there is a number following the ellipses, then the sequence ends at that number: B={1,3,5,7,...21} is a set of odd numbers from 1 to 21.

A colon in a pair of curly brackets is used to identify elements in a set. For example, {n : n>7} means *values of n such that the elements of the set* are greater than 7.

Sets can be used to define a set of points eg C = {(*x*, *y*) : *y* = 3*x*^{2} + 4} which defines a set of coordinates that satisfies the given equation.

There are four groups of numbers that are often used in sets.

**ℕ** is the set of natural, positive numbers. If the set includes zero, it is normally shown as ℕ_{0}; if the set does not include zero, then it should be shown as ℕ_{1}.

**ℤ** is the set of all integers.

**ℚ** is the set of Rational numbers (numbers that can be written as a fraction, where the numerator and denominator of the fraction are both integers.

**ℝ** is the set of real numbers, and includes π, √2 etc.

Given a set K = {n ∈ ℕ: n≤10} and a set L = {3,4,5,...20}, what is n(K ∩ L)?

The set K is the set of natural numbers that are less than or equal to 10: K = {1,2,3,4,5,6,7,8,9,10}.

L= {3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}.

Elements in both sets K ∩ L = {3,4,5,6,7,8,9,10}.

The number of elements is 8.

Answer: n(K ∩ L) = 8

Given ε = {1, 2, 3, … 20}

Set A is a list of prime numbers from 2 to 20

Set B is defined as {n: 0 < n < 7}

What is the probability P(A ∩ B)?

A = {2, 3, 5, 7, 11, 13, 17, 19}

B = {1, 2, 3, 4, 5, 6}

A ∩ B = {2, 3, 5}, and n(A ∩ B) = 3

The Universal Set has 20 elements, so probability is `frac(3)(20)` or 0.15

Answer: 0.15

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