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H101:
Intro to Informatics &ComputingNina Onesti
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Review
Problem solving
Wicked & Tame Problems
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Problem Solving: The Process
problem solution
problem solving activities
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Traditional process
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Modified process
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Review?
Whats the first and most important step in problem solving?
What is an example method?
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Wicked & Tame Problems
Wicked Problems Tame Problems
Difficult or impossible to
solve because of incomplete,
contradictory, and changing
requirements that are often
difficult to recognize.
Example:
Designing a safe way forstudents to cross 10thstreet
Fixing healthcare
- Has a definite solution
- Has a solution that can be
evaluated
- Is defined and stable
Example:
Provide detailed
instructions for making apeanut butter and jelly
sandwich
Chess game
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Taming a wicked problem
1. Define the problem
2. Thought exercise: the problem does not exist
3. Find a way to measure the success of a solution
4. Find similarities to another problem/solution
5. Stop trying to solve it (for now)
6. Change the options to either/or
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Next step in problem solving
Logical Thinking and Critical Thinking
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Soduku discussion
Complete the soduku puzzle, and list the steps you took to complete it or theRULES for THIS specific Soduku puzzle
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Soduku discussion
RULES
1) Must use the #s 1-4
In every row
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Soduku discussion
RULES
1) Must use the #s 1-4
In every column
In every row
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Soduku discussion
RULES
1) Must use the #s 1-4
In every smaller box
In every column
In every row
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Soduku discussion
RULES
1) Must use the #s 1-4
In every smaller box
In every column
In every row
2) No Repeats
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Logical Thinking
Requires a language where:
Each phrase has one and only one meaning
Giving directions, etc
The rules are clear and do not change
Structured
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Propositions
Propositions
Think about sentences that are either true or false
Grass is green
2+1=6
Close the door!
X is greater than 2
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Propositional Logic
Conjunction
Disjunction
Negation
Where:
0 = false
1 = true
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Conjunction (^) (*)
And
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Conjunction (and) (^) (*)
P Q P^Q
0 00 1
1 0
1 1
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Conjunction (and) (^) (*)
P Q P^Q
0 0 00 1
1 0
1 1
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Conjunction (and) (^) (*)
P Q P^Q
0 0 00 1 0
1 0
1 1
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Conjunction (and) (^) (*)
P Q P^Q
0 0 00 1 0
1 0 0
1 1
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Conjunction (and) (^) (*)
P Q P^Q
0 0 00 1 0
1 0 0
1 1 1
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Disjunction (v) (+)
Or
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Disjunction (or) (v) (+)
P Q PvQ
0 00 1
1 0
1 1
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Disjunction (or) (v) (+)
P Q PvQ
0 0 00 1
1 0
1 1
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Disjunction (or) (v) (+)
P Q PvQ
0 0 00 1 1
1 0
1 1
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Disjunction (or) (v) (+)
P Q PvQ
0 0 00 1 1
1 0 1
1 1
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Disjunction (or) (v) (+)
P Q PvQ
0 0 00 1 1
1 0 1
1 1 1
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Negation ()
Not
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Negation ()
P P
01
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Negation ()
P P
0 11 0
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Truth Tables (T-tables)
Demonstrate all possible outcomes of a propositional
statement and the relationship between variables
Variables are listed as letters in our Truth Tables
For example, P and Q
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Truth Table example:
(P v Q) = P or Q
P Q P v Q
0 0 0
0 1 1
1 0 1
1 1 1
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How we ALWAYS start Truth
Tables
P Q
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How we ALWAYS start Truth
Tables
P Q
0 0
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How we ALWAYS start Truth
Tables
P Q
0 00 1
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How we ALWAYS start Truth
Tables
P Q
0 00 1
1 0
h
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How we ALWAYS start Truth
Tables
P Q
0 00 1
1 0
1 1
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Truth Table example:
(P v Q) ^ Q = not (P or Q) and Q
P Q
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Truth Table example:
(P v Q) ^ Q
P Q
0 0
0 11 0
1 1
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Truth Table example:
(P v Q) ^ Q
P Q P v Q
0 0
0 11 0
1 1
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Truth Table example:
(P v Q) ^ Q
P Q P v Q
0 0 0
0 1 11 0 1
1 1 1
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Truth Table example:
(P v Q) ^ Q
P Q P v Q (P v Q)
0 0 0
0 1 11 0 1
1 1 1
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Truth Table example:
(P v Q) ^ Q
P Q P v Q (P v Q)
0 0 0 1
0 1 11 0 1
1 1 1
h bl l
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Truth Table example:
(P v Q) ^ Q
P Q P v Q (P v Q)
0 0 0 1
0 1 1 01 0 1
1 1 1
h bl l
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Truth Table example:
(P v Q) ^ Q
P Q P v Q (P v Q)
0 0 0 1
0 1 1 01 0 1 0
1 1 1
T h T bl l
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Truth Table example:
(P v Q) ^ Q
P Q P v Q (P v Q)
0 0 0 1
0 1 1 01 0 1 0
1 1 1 0
T h T bl l
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Truth Table example:
(P v Q) ^ Q
P Q P v Q (P v Q) (P v Q) ^ Q
0 0 0 1
0 1 1 01 0 1 0
1 1 1 0
T h T bl l
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Truth Table example:
(P v Q) ^ Q
P Q P v Q (P v Q) (P v Q) ^ Q
0 0 0 1 0
0 1 1 01 0 1 0
1 1 1 0
T h T bl l
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Truth Table example:
(P v Q) ^ Q
P Q P v Q (P v Q) (P v Q) ^ Q
0 0 0 1 0
0 1 1 0 01 0 1 0
1 1 1 0
T h T bl l
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Truth Table example:
(P v Q) ^ Q
P Q P v Q (P v Q) (P v Q) ^ Q
0 0 0 1 0
0 1 1 0 01 0 1 0 0
1 1 1 0
T th T bl l
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Truth Table example:
(P v Q) ^ Q
P Q P v Q (P v Q) (P v Q) ^ Q
0 0 0 1 0
0 1 1 0 01 0 1 0 0
1 1 1 0 0
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Logical Outcomes
Tautology
ALL 1s (or ALL True)
Contradition
ALL 0s (or ALL False)
Contingency
ANY mix of 0s and 1s
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(P) ^ [(P ^ Q)]
P Q
0 0
0 1
1 0
1 1
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(P) ^ [(P ^ Q)]
P Q P
0 0
0 1
1 0
1 1
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(P) ^ [(P ^ Q)]
P Q P
0 0 1
0 1 1
1 0 0
1 1 0
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(P) ^ [(P ^ Q)]
P Q P (P ^ Q)
0 0 1
0 1 1
1 0 0
1 1 0
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(P) ^ [(P ^ Q)]
P Q P (P ^ Q)
0 0 1 0
0 1 1 0
1 0 0 0
1 1 0 1
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(P) ^ [(P ^ Q)]
P Q P (P ^ Q) (P ^ Q)
0 0 1 0
0 1 1 0
1 0 0 0
1 1 0 1
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(P) ^ [(P ^ Q)]
P Q P (P ^ Q) (P ^ Q)
0 0 1 0 1
0 1 1 0 1
1 0 0 0 1
1 1 0 1 0
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(P) ^ [(P ^ Q)]
P Q P (P ^ Q) (P ^ Q) (P) ^ [(P ^ Q)]
0 0 1 0 1
0 1 1 0 1
1 0 0 0 1
1 1 0 1 0
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(P) ^ [(P ^ Q)]
P Q P (P ^ Q) (P ^ Q) (P) ^ [(P ^ Q)]
0 0 1 0 1 1
0 1 1 0 1 1
1 0 0 0 1 0
1 1 0 1 0 0
CONTINGENCY
[ ( P) ^ ( Q) ] v (P ^ Q)
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[ (P) ^ (Q) ] v (P ^ Q)
(P ^ Q) ^ [P v (Q)]
P Q P
0 0
0 1
1 0
1 1
[ ( P) ^ ( Q) ] v (P ^ Q)
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[ (P) ^ (Q) ] v (P ^ Q)
(P ^ Q) ^ [P v (Q)]
P Q P
0 0 1
0 1 1
1 0 0
1 1 0
[ ( P) ^ ( Q) ] v (P ^ Q)
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[ (P) ^ (Q) ] v (P ^ Q)
(P ^ Q) ^ [P v (Q)]
P Q P Q
0 0 1
0 1 1
1 0 0
1 1 0
[ ( P) ^ ( Q) ] v (P ^ Q)
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[ (P) ^ (Q) ] v (P ^ Q)
(P ^ Q) ^ [P v (Q)]
P Q P Q
0 0 1 1
0 1 1 0
1 0 0 1
1 1 0 0
[ (P) ^ (Q) ] v (P ^ Q)
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[ (P) (Q) ] v (P Q)
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q)
0 0 1 1
0 1 1 0
1 0 0 1
1 1 0 0
[ (P) ^ (Q) ] v (P ^ Q)
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[ (P) (Q) ] v (P Q)
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q)
0 0 1 1 1
0 1 1 0 0
1 0 0 1 0
1 1 0 0 0
[ (P) ^ (Q) ] v (P ^ Q)
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70/100
[ (P) (Q) ] v (P Q)
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q)
0 0 1 1 1
0 1 1 0 0
1 0 0 1 0
1 1 0 0 0
[ (P) ^ (Q) ] v (P ^ Q)
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[ (P) (Q) ] v (P Q)
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q)
0 0 1 1 1 0
0 1 1 0 0 0
1 0 0 1 0 0
1 1 0 0 0 1
[ (P) ^ (Q) ] v (P ^ Q)
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[ (P) (Q) ] v (P Q)
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q) [(P) ^ (Q)] v (P ^ Q)
0 0 1 1 1 0
0 1 1 0 0 0
1 0 0 1 0 0
1 1 0 0 0 1
[ (P) ^ (Q) ] v (P ^ Q)
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[ (P) (Q) ] v (P Q)
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q) [(P) ^ (Q)] v (P ^ Q)
0 0 1 1 1 0 1
0 1 1 0 0 0 0
1 0 0 1 0 0 0
1 1 0 0 0 1 1
CONTINGENCY
[ (P) ^ (Q) ] v (P ^ Q)
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[ (P) (Q) ] v (P Q)
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q) [(P) ^ (Q)] v (P ^ Q)
0 0 1 1 1 0 1
0 1 1 0 0 0 0
1 0 0 1 0 0 0
1 1 0 0 0 1 1
P Q
0 0
0 1
1 0
1 1
CONTINGENCY
[ (P) ^ (Q) ] v (P ^ Q)
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[ (P) (Q) ] v (P Q)
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q) [(P) ^ (Q)] v (P ^ Q)
0 0 1 1 1 0 1
0 1 1 0 0 0 0
1 0 0 1 0 0 0
1 1 0 0 0 1 1
P Q (P ^ Q)
0 0
0 1
1 0
1 1
CONTINGENCY
[ (P) ^ (Q) ] v (P ^ Q)
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[ (P) (Q) ] v (P Q)
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q) [(P) ^ (Q)] v (P ^ Q)
0 0 1 1 1 0 1
0 1 1 0 0 0 0
1 0 0 1 0 0 0
1 1 0 0 0 1 1
P Q (P ^ Q)
0 0 0
0 1 0
1 0 0
1 1 1
CONTINGENCY
[ (P) ^ (Q) ] v (P ^ Q)
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[ ( ) ( Q) ] ( Q)
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q) [(P) ^ (Q)] v (P ^ Q)
0 0 1 1 1 0 1
0 1 1 0 0 0 0
1 0 0 1 0 0 0
1 1 0 0 0 1 1
P Q (P ^ Q) (P ^ Q)
0 0 0
0 1 0
1 0 0
1 1 1
CONTINGENCY
[ (P) ^ (Q) ] v (P ^ Q)
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[ ( ) ( Q) ] ( Q)
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q) [(P) ^ (Q)] v (P ^ Q)
0 0 1 1 1 0 1
0 1 1 0 0 0 0
1 0 0 1 0 0 0
1 1 0 0 0 1 1
P Q (P ^ Q) (P ^ Q)
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0
CONTINGENCY
[ (P) ^ (Q) ] v (P ^ Q)
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[ ( ) ( ) ] ( )
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q) [(P) ^ (Q)] v (P ^ Q)
0 0 1 1 1 0 1
0 1 1 0 0 0 0
1 0 0 1 0 0 0
1 1 0 0 0 1 1
P Q (P ^ Q) (P ^ Q) (Q)
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0
CONTINGENCY
[ (P) ^ (Q) ] v (P ^ Q)
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[ ( ) ( ) ] ( )
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q) [(P) ^ (Q)] v (P ^ Q)
0 0 1 1 1 0 1
0 1 1 0 0 0 0
1 0 0 1 0 0 0
1 1 0 0 0 1 1
P Q (P ^ Q) (P ^ Q) (Q)
0 0 0 1 1
0 1 0 1 0
1 0 0 1 1
1 1 1 0 0
CONTINGENCY
[ (P) ^ (Q) ] v (P ^ Q)
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[ (
(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q) [(P) ^ (Q)] v (P ^ Q)
0 0 1 1 1 0 1
0 1 1 0 0 0 0
1 0 0 1 0 0 0
1 1 0 0 0 1 1
P Q (P ^ Q) (P ^ Q) (Q) P v (Q)
0 0 0 1 1
0 1 0 1 0
1 0 0 1 1
1 1 1 0 0
CONTINGENCY
[ (P) ^ (Q) ] v (P ^ Q)
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(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q) [(P) ^ (Q)] v (P ^ Q)
0 0 1 1 1 0 1
0 1 1 0 0 0 0
1 0 0 1 0 0 0
1 1 0 0 0 1 1
P Q (P ^ Q) (P ^ Q) (Q) P v (Q)
0 0 0 1 1 1
0 1 0 1 0 0
1 0 0 1 1 1
1 1 1 0 0 1
CONTINGENCY
[ (P) ^ (Q) ] v (P ^ Q)
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(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q) [(P) ^ (Q)] v (P ^ Q)
0 0 1 1 1 0 1
0 1 1 0 0 0 0
1 0 0 1 0 0 0
1 1 0 0 0 1 1
P Q (P ^ Q) (P ^ Q) (Q) P v (Q) (P ^ Q) ^ [P v (Q)]
0 0 0 1 1 1
0 1 0 1 0 0
1 0 0 1 1 1
1 1 1 0 0 1
CONTINGENCY
[ (P) ^ (Q) ] v (P ^ Q)
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(P ^ Q) ^ [P v (Q)]
P Q P Q (P) ^ (Q) (P ^ Q) [(P) ^ (Q)] v (P ^ Q)
0 0 1 1 1 0 1
0 1 1 0 0 0 0
1 0 0 1 0 0 0
1 1 0 0 0 1 1
P Q (P ^ Q) (P ^ Q) (Q) P v (Q) (P ^ Q) ^ [P v (Q)]
0 0 0 1 1 1 1
0 1 0 1 0 0 0
1 0 0 1 1 1 1
1 1 1 0 0 1 0
CONTINGENCY
CONTINGENCY
NOT Logically Equivalent!!!
Ci i
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Circuits
AND
P^Q
OR
PvQ
NOT
P
P
Q
P
Q
P
( P) [ (P ^ Q)]
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(P) v [ (P ^ Q)]
P
( P) [ (P ^ Q)]
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(P) v [ (P ^ Q)]
P
Q
P
( P) [ (P ^ Q)]
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(P) v [ (P ^ Q)]
P
Q
P
( P) [ (P ^ Q)]
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(P) v [ (P ^ Q)]
P
Q
P
( P) [ (P ^ Q)]
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(P) v [ (P ^ Q)]
P
Q
( P) [ (P ^ Q)]
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(P) v [ (P ^ Q)]
P
Q
What is the propositional logic
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P
Q
P
Q
p p g
statement for this circuit?
(P ^ Q)
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P
Q
P
Q
(P ^ Q)
(P Q)(P ^ Q)
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P
Q
P
Q
(P v Q)(P ^ Q)
(P Q)(P ^ Q)
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P
Q
P
Q
(P v Q)v(P ^ Q)
(P Q) ][ (P ^ Q)
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P
Q
P
Q
(P v Q) ]v[ (P ^ Q)
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P
Q
P
Q
(P ^ Q)
(P) ^ (Q)
Jargon
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Jargon
Algorithms vs. Heuristics
BOTH are ways to do something/completing a task
Instructions
Process
Etc
Algorithms
Structured
Sequential (1, 2, 3)
Hueristics General guidelines
Rule of thumb
Common practices
Critical Thinking
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Critical Thinking
Creative Using past experiences
Making connections
Being able to formulate answers
Final Wrap Up
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Final Wrap Up
Please visit Oncourse ASSIGNMENTS for this lecture (where youdownloaded this lecture) and complete the LECTURE ASSESSMENTin the submission box provided.
Practice some critical thinking
Make up a VENDING MACHINEat minimum:
- Draw a picture of it
- Explain what it vends
- Must be for a specific location (ex. Airport, dorm, etc)
- Must be for a specific reason (ex. Food, shelter, etc)- Take a photo of your drawing & upload it to the LECTURE
ASSESSMENT under Oncourse/Assignment (scan or photo is fine)
- MUST BE CLASS APPROPRIATE
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