M1. Intro To DISMATH Flashcards
___ is the study of mathematical structures that are countable or otherwise distinct and separable
Discrete mathematics
It is based upon continuous number line or the real numbers. It is characterized by the fact that between any two numbers, there are almost always an infinite set of numbers. F
Continuous Mathematics
It involves distinct values; i.e. between any two points, there are a countable number of points.
Discrete Mathematics
__ is the mathematical language of computer science
Discrete Mathematics
____is at the heart of problem solving
Mathematics
To justify why a particular way of solving a problem is correct or efficient (i.e., better than another way) requires analysis with a ____.
well-defined mathematical model
Applications of Discrete Mathematics
Storing files in a computer
Scheduling problems
Computer graphics
Networks
Analog clocks
Cryptography
Cellular communication
Railway planning
Digital image processing
Google maps
Web searches
__ is a science of necessary inference or study of reasoning
Logic
Logic identifies valid ____
mathematical argument
__ dealt with arguments in the natural language used by humans.
Logic
____is a kind of language, where everything is designed to have a precise
meaning.
Mathematical Logic
Logic comes into computer science in many different ways:
Digital circuit logic
Proof of correctness of programs, verification
Automated reasoning in artificial intelligence
Database query language
___ are the meanings of statements
propositions
Proposition is a ____ statement that is either true or false but not both
declarative
We say that the truth value of a proposition is either true (T) or false (F) which corresponds to___in digital circuits
1 and 0
Proposition or not?
The current president of the United States is Joe Biden.
This is a proposition because it is a declarative sentence and we can determine its truth value by checking facts that will prove that Joe Biden is the incumbent president of the US. At this point, the truth value of this proposition is TRUE.
Proposition or not?
Do you have extra paper?
This is NOT a proposition because it is not a declarative statement. It is an interrogative statement and we cannot determine its truth value to be true or false
Discrete Mathematics also has its own sets of operations and operators or sometimes called ___that we can use on propositions
connectives
__ are grammatically independent expressions of information
Simple propositions
___ consist of two or more propositions joined by connectives such as “and”, “or”, “but” and others.
Compound propositions
(^) This is a __ connective
and
(v) This is a __ connective
or
(~) This is a __ connective
not
(->) This is a __ connective
implies (implications)