Alg1231W10T1 - Basic set theory

Thursday, 27 September 2018

5:12 PM

Consider two sets A and B, both subsets Of a universal set S. The set A c is known as the complement O Of the set A. In plain English, this is the set Of elements in the universal set S which do not lie in the set A. Using set notation this can be compactly written as The set A n B is known as the intersection set notation this can be compactly written as The set A U B is known as the union Using set notation this can be compactly written as The set A — B is known as the difference O Of the sets A and B. In plain English, this is the set Of elements common to both A and B. Using O Of the sets A and B. In plain English, this is the setof elements which are in A or B (or both!!). O of the sets A and B. In plain English, this is the set of elements which lie in the set A but do not lie in B. In other words, it is the set A with the elements from B removed. Using set notation this can be compactly written as A — B = {x G S : x G A andx B}. Note that A — B = A n BC.

 

Match the shaded regions in the following diagrams to their definitions.

 

Machine generated alternative text:

 

e b Consider the set A = {a, b, f} and the set B = {d, e, f}. These are subsets of the universal set S Enter the following sets: o Note: the Maple syntax for the empty set is { y.

 

Let the universal set be Consider the following three sets Enter the following sets. s = {x e Z: 1 s x s 12} = 10, 11, 12}. A — {c G S : is a multiple Of 3}, B = {c S : is a multiple of 7}, C = {x e S : is prime}.

 

If we flip a coin 3 times, we can record the outcome as a string of H (heads) and T (tails). Thus getting a head, then another head, and then a tail would be recorded as H HT. Clearly there are a total of 8 O possible sequences. • Exactly • Exactly • Exactly • Exactly 3 3 O of these outcomes consists of all heads. of these outcomes involve 2 heads and 1 tail. of these outcomes involve 1 head and 2 tails. of these outcomes involve 3 tails. These numbers should be familiar, they are the binomial coefficients , which can be read as 'n choose k'. In this case n If we flipped a coin 7 times, there would be 128 be 35 O different possible outcomes. The number of these involving exactly 4 heads and 3 tails would

 

Machine generated alternative text: Sets A and B are disjoint precisely when [select all that apply] they contain no common elements O they don't like being together. Which of the following are disjoint sets? {4, 7, 18, 10, -18, -5, —3} and {6, 5, 8, -10} The set of all primes, and the set of all even numbers O {1, 13, 2, 9, 10} and 13, 17} The set of students taking Math1231 this semester, and the set of students taking Math1021 this semester. {people who love Game of Thrones} and {people who hate Game of Thrones}. Hint: see the Math1231 course homepage to check what course exclusions apply. Sets Al A2,... Ak partition a set B precisely when:

 

Machine generated alternative text: and @ the sets Al ,A2, ... , Ak are pairwise disjoint Which of the following are examples of partitions? O Al = Al Al {1, = {2, = {3, 4} are a partition of B {1, = {2, 4} are a partition of B — {1, 2, 3,4}. {girls taking MA THI 231} and .42 = {boys taking MATH1231} are a partition of B — {students taking MA THI 231}. MATH1231 students who sometimes do their online tutorials on Sunday night MATH1231 students who never do their online tutorials on Sunday night MATH 1231 students who always do their online tutorials on Sunday night are a partition of B — {the MATH1231 set of students}.

 

 

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