Geometry
Notes
Name_______________________________
Symbolic Notation & Venn Diagrams
Recall conditional statements!
Given the if-then statement “If Peggy’s riding her bike, then she’s wearing her helmet,” find the
following:
Converse –
Inverse –
Contrapositive –
Symbolic Notation:
Conditional
If p, then q.
p  q
Converse
If q, then p.
q  p
Inverse
If not p, then not q.
p q
Contrapositive
If not q, then not p.
q p
Biconditional
p if and only if q
p  q
p and q
pq
p or q
pq
What about the other symbols???
(  ) means “implies”
  means negation – “not p” is written
p
( ) means “therefore”
Examples 1 – 4: Let p represent “the car is running” and let q represent “the key is in the
ignition.” Turn the given statements into symbolic notation.
1. If the car is running, then the key is in the ignition.
2. If the key is not in the ignition, then the car is not running.
3. If the car is not running, then the key is not in the ignition.
4. The key is in the ignition and the car is running.
Practice 5 – 9: Let p represent “you have a library card” and let q represent “you can check
out books.” Write the appropriate statement to match the symbolic notation.
5. p  q
6.
q p
7. q  p
8.
p q
9. p  q
Venn Diagrams
Venn diagrams are used to show relationships between things.
All, Always, Every
Some, Sometimes
Never, No, None
q
p
q
p
q
p
All elements of p
are elements of q.
Some elements of p
are elements of q.
There is no relationship
between p and q.
Examples 1 – 2: Draw a Venn diagram for each example using the given information.
1. Some bicycles are blue.
2. All fish swim.
Examples 3 – 6: Shade the indicated region on each Venn diagram.
3. q
4. p  q
p
q
p
q
5. p  q
6. p 
p
q
q
p
q
Examples 7 – 15: On a recent survey, students were asked if they ice skate, snowboard, or
ski. The Venn diagram below shows the results of the survey.
7. How many students ski or snowboard? __________
8. How many students ice skate or ski? __________
9. How many students ice skate, ski, and snowboard? __________
10. How many students to not ski or ice skate? __________
11. How many students just snowboard? __________
12. How many students do not ice skate, ski, or snowboard? __________
13. How many students ice skate? __________
14. How many students do not snowboard? __________
15. How many students took the survey? __________