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Language of Logic 1-2B
What is the difference between the words:
All
Some
None
What is a counterexample?
A counterexample shows that a statement is
false.
Go to The Mad Tea Party on p. 19
The Mad Tea Party on p. 19
What was Alice’s false statement?
What counterexamples to Alice’s logic were
given by the Mad Hatter, the March Hare,
and the Dormouse?
What is the difference between “I mean what
I say” and “I say what I mean”?
If you had attended the tea party, what
counterexample to Alice’s logic could you
have added to the conversation?
Give a counterexample that
disproves the conjecture.
• All birds can fly.
• All four-sided figures (quadrilaterals) are
rectangles.
When making a conjecture, you must be
careful to say exactly what you mean. You
need to use common terms like all, some,
and none very carefully when making logical
statements.
All dogs in town need a license.
All squares are rectangles.
Venn diagram--all
Some
Some dogs have fleas.
Some quadrilaterals are squares.
Venn Diagram--some
_____ Triangles Are…
• All triangles…
• Some triangles…
• No triangle…
And---Or
Use the words and, or to link logical
statements.
AND—both parts must be true for the
combined statement to be true.
OR—one part can be true or both parts are
true in mathematics.
And
Jessie will compete in the long jump and she
will run the 100 meters.
True when 1.
False when 1.
2.
3.
OR
Juan is going to the store or he is going
swimming.
True when 1.
2.
False when 1.
Assignment 1-2B
p. 28, 1-12, 25-29