This document defines key logical terms: counter-example, AND/OR statements, Venn diagrams, conditional statements, hypotheses, conclusions, converses, inverses, contrapositives, inductive reasoning, and deductive reasoning. Examples and truth tables are provided to illustrate each term. Inductive reasoning moves from specific to general observations based on past experiences, while deductive reasoning moves from general rules or statements to specific conclusions.

2. 1.Term: Counter-Example
Definition: An example that
contradicts a statement.
( Shows a statement to be false)
Diagram/Truth Table/Example
Statement: all rectangles are squares.
Counter example

3. 2.Term: AND Statement
Definition: Two statements joined
by the word “and”. The statement
is true only if both statements are
true.
P
Q
P and Q
T
T
T
T
F
F
F
T
F
F
F
F

4. 3.Term: OR Statement
Definition: Two statements joined
by the word “or”. The statement is
true if either or both of the
statements are true.
P
Q
P or Q
T
T
T
T
F
T
F
T
T
F
F
F

5. 4.Term: Venn Diagram
Definition: Used to show
relationships between sets or
groups of things.
Diagram/Truth Table/Example

6. 5.Term: Conditional Statement
Definition: If, then statement. If p
then q. An alternate statement: q
if p. p implies q
P
Q
If P, then Q
T
T
T
T
F
F
F
T
T
F
F
T

7. 6.Term: Hypothesis
Definition: The if “part”
Diagram/Truth Table/Example: If I cut myself
peeling onions, then I will bleed.

8. 7.Term: Conclusion
Definition: The then “part”
Diagram/Truth Table/Example: Diagram/Truth
Table/Example: If cut myself peeling onions,
then I will bleed.

9. Term: Converse
Definition: When the original
hypothesis and conclusion are
switched. If q, then p.
Diagram/Truth Table/Example: If I cut
myself peeling onions, then I will bleed.
becomes If I bleed, then I cut myself
peeling onions.

10. 8. Term: Inverse
Definition: When you negate
both the hypothesis and
conclusion.
Diagram/Truth Table/Example: If I cut myself
peeling onions, then I will bleed. Becomes, If
I did not cut myself peeling onions, then I will
not bleed.

11. 9.Term: Contrapositive
Definition: When you negate both
the hypothesis and conclusion and
switch their original position
Diagram/Truth Table/Example: If I cut
myself peeling onions, then I will bleed.
Becomes, If I did not bleed, then I did
not cut myself peeling onions

12. Term: Inductive Reasoning
Definition: Based on
• Observations
• Past experience
• Moves from specific to general
observations
• Is useful in providing conjecture or
hypothesis
• Does not always lead to a valid
conclusion

13. Term: Inductive Reasoning (cont)
Diagram/Truth Table/Example:
You observe that for the last 5
weeks in math, you have had a
quiz on Tuesday. As today is
Monday, you conclude that
tomorrow, there will be a quiz in
math.

14. Term: Deductive Reasoning
Definition:
• Based on facts, definitions,
postulates, properties and
theorems
• Moves from general to specific
• Is useful in providing conjectures
• Always leads to a valid conclusion,
if the assumptions are true

15. Term: Deductive Reasoning (cont)
Diagram/Truth Table/Example
On your geometry progress
report, the lowest grade was a
92. You conclude that your
average in geometry is at least
92

16. Term:
Definition:
Diagram/Truth Table/Example