Readings for Session 5 – (Continued)  

Definitions for "Or" and "And"

Definition of “or” in Mathematics:  The phrase “a or b” means we have only a, or only b, or both a and b.

Example:  The statement, “The bicycle is red or it is a 10-speed.” means that the bicycle could be only red, it could be only a 10-speed, or it could be both red and a 10-speed.  This is the inclusive use of “or”.

When working with sets, the word “or” corresponds to the set operation union.

Example:  { x : x is a factor of 12 or x is a factor of 10}

= { x : x is a factor of 12} ∪ { x : x is a factor of 10}

= {1, 2, 3, 4, 6, 12} ∪ {1, 2, 5, 10}

=  {1, 2, 3 ,4, 5, 6, 10, 12}

        Unlike the word “or”, the word “and” usually is not interpreted more than one way. For example, when we make a statement such as “Pat wants mustard and ketchup on the hotdog.”, we understand that Pat wants both condiments. But, to make sure the interpretation is clear, we define the meaning of “and” for mathematics.

Definition of  “and” in Mathematics:  The phrase “a and b” means “both a and b.” 

Example:  The statement, “You must make less than $10,000 a year and live in Minnesota to qualify for this grant.” means that you only qualify for the grant if you satisfy both conditions:  you make less than $10,000 a year AND ALSO you live in Minnesota.

When working with sets, the word “and” corresponds to the set operation intersection.

Example:  { x :  x is a factor of 12 and x is a factor of 10}

=  { x :  x is an factor of 12} ∩ { x : x is a factor of 10}

=  {1, 2, 3, 4, 6, 12} ∩ {1, 2, 5, 10}

=  {1, 2}

Return to Session 5 - Union.
Return to Session 5 - Intersection.

      

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