 Discrete Structures at Jackson State University | Flashcards & Summaries

Suggested languages for you: # 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

• 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

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

• 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. ### Erstelle und finde Lernmaterialien auf StudySmarter.

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