Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.1, Slide 1 3 3 Logic The Study of...

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Section 3.1, Slide 1

33 Logic

The Study of What’s True or False or Somewhere in Between



Statements, Connectives, and Quantifiers

3.1

• Identify statements in logic

• Represent statements symbolically using five connectives

(continued on next slide)



Statements, Connectives, and Quantifiers

3.1

• Understand the difference between the universal and existential quantifiers

• Write the negations of quantified statements

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.1, Slide 4

Statements in Logic

• In symbolic logic, we only care whether statements are true or false – not their content.


Statements in Logic

• Examples of statements:


Statements in Logic

• Examples of non-statements:


Statements in Logic

• Note that (a)-(d) fall into 2 categories:– Simple statements containing a single idea ((a) and

(c)).– Compound statements containing several ideas ((b)

and (d)).


Statements in Logic


Connectives

• The connectives used in logic generally fall into five categories:– Negation– Conjunction– Disjunction– Conditional– Biconditional


Connectives

(example on next slide)


Connectives

• Negation Example:


Connectives

• Example:


Connectives


Connectives

• Example:


Connectives


Quantifiers

• A quantifier tells us “how many” and fall into two categories.– Universal quantifiers– Existential quantifiers


Quantifiers


Negating Quantifiers

• Suppose we want to negate the statement “All professional athletes are wealthy.” (universal)

Correct: “Some athletes are not wealthy” or “Not all athletes are wealthy.” (both existential)

Incorrect: “All athletes are not wealthy.” (universal)



• Negate the statement “Some students will get a scholarship.” (existential)

Correct: “No students will get a scholarship.” (universal)

Incorrect: “Some students will not get a scholarship.” (existential)

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.1, Slide 1 3 3 Logic The Study of...

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