Discrete Structures at Jackson State University | Flashcards & Summaries

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Lernmaterialien für discrete structures an der Jackson State University

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Informal Logic (Critical Thinking)


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– is concerned with evaluating premises and inferences,

 – evaluates inferences on a sliding scale, – considers arguments in the "natural language"

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Logic

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  • proper or reasonable way of thinking about or understanding something
  • particular way of thinking about something
  • the science that studies the formal processes used in thinking and reasoning
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contrapositive

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  • p → q is  ~q → ~p 

If it snows, the traffic moves slowly

  •  p: it snows
  • q: traffic moves slowly 

Contrapositive

– If the traffic does not move slowly then it does not snow 

~q → ~p

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Logical connectives:

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– Negation 

– Conjunction

 – Disjunction 

– Implication 

– Biconditional

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graph


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the mathematical version of interrelated objects

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Propositional logic

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• The Simplest logic

 • 7 is odd • 1 + 1 = 4 •

 If it is raining, then the ground is wet 

• Our professor is from Mars 

• x is even 

• Please, close the door 

• This sentence is False

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Conjunction (∧) and

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  • Let p and q be propositions.
  •  The proposition "p and q" denoted by p∧q, is true when both p and q are true and is false otherwise. 
  • The proposition p ∧ q is called the conjunction of p and q.
  • It is raining today and 2 is a prime number.
  • 2 is a prime number and 5+2 = 7
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Discrete mathematics

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study of mathematical structures and objects that are fundamentally discrete

  • object is discrete if it is not continuous

Examples of objects with discrete values are

– integers, graphs, or statements in logic

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elements (or members) of the set.

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objects in a set

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lemma

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less important theorem that is helpful in a proof.

  • Stepping stone on the path to proving a theorem
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statement (or proposition)

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a declarative sentence that is either true or false, but not both.

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set

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unordered collection of objects.

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Q:

Informal Logic (Critical Thinking)


A:

– is concerned with evaluating premises and inferences,

 – evaluates inferences on a sliding scale, – considers arguments in the "natural language"

Q:


Logic

A:
  • proper or reasonable way of thinking about or understanding something
  • particular way of thinking about something
  • the science that studies the formal processes used in thinking and reasoning
Q:

contrapositive

A:
  • p → q is  ~q → ~p 

If it snows, the traffic moves slowly

  •  p: it snows
  • q: traffic moves slowly 

Contrapositive

– If the traffic does not move slowly then it does not snow 

~q → ~p

Q:


Logical connectives:

A:

– Negation 

– Conjunction

 – Disjunction 

– Implication 

– Biconditional

Q:

graph


A:

the mathematical version of interrelated objects

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Q:

Propositional logic

A:

• The Simplest logic

 • 7 is odd • 1 + 1 = 4 •

 If it is raining, then the ground is wet 

• Our professor is from Mars 

• x is even 

• Please, close the door 

• This sentence is False

Q:


Conjunction (∧) and

A:
  • Let p and q be propositions.
  •  The proposition "p and q" denoted by p∧q, is true when both p and q are true and is false otherwise. 
  • The proposition p ∧ q is called the conjunction of p and q.
  • It is raining today and 2 is a prime number.
  • 2 is a prime number and 5+2 = 7
Q:

   

Discrete mathematics

A:

study of mathematical structures and objects that are fundamentally discrete

  • object is discrete if it is not continuous

Examples of objects with discrete values are

– integers, graphs, or statements in logic

Q:


elements (or members) of the set.

A:

objects in a set

Q:


lemma

A:

less important theorem that is helpful in a proof.

  • Stepping stone on the path to proving a theorem
Q:

statement (or proposition)

A:

a declarative sentence that is either true or false, but not both.

Q:


set

A:

unordered collection of objects.

discrete structures

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