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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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[ (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