LOGIC & TRUTH.pptx PROPOSITIONAL LOGIC AND ETC.

• Logic is like a set of rules for thinking and figuring things out.
• It's a way of using information to come to a sensible conclusion.
• Logic helps us sort through all of that and decide what to believe or accept as
true.
• It's like a guide that tells us when an argument makes sense and when it
doesn't.
What is Logic?

EXAMPLE(S):
1. "All mammals have fur. Dogs are mammals.
Therefore, ____ have ___,"

EXAMPLE(S):
Therefore, Dogs have fur."
We're using logic to connect the dots and reach a reasonable
conclusion based on what we know.

EXAMPLE(S):
2. “All humans are mortal. Marc is a _____.
Therefore, ____ is _____.

EXAMPLE(S):
2. “All humans are mortal. Marc is a mortal.
Therefore, Marc is human.

EXAMPLE(S):
"All clouds are made of cheese.
Cats like to sleep on clouds. Therefore, cats like to sleep on
cheese."

EXAMPLE(S):
cheese."
This sentence lacks sense because it makes an illogical
connection between clouds and cheese. What does it imply?

EXAMPLE(S):
cheese."
THE SENTENCE DOES NOT MAKE SENSE!

EXAMPLE(S):
cheese."
"All clouds are made of marshmallows.
Fish enjoy swimming in clouds. Therefore, fish enjoy
swimming in marshmallows."

EXAMPLE(S):
"All students who study hard get good grades. Sarah studies
hard. Therefore, Sarah will likely get good grades."
This sentence makes sense because it follows a logical
structure.

TYPES OF LOGIC
DEDUCTIVE, INDUCTIVE, & SYMBOLIC

DEDUCTIVE LOGIC
Deductive logic is a way of thinking where if you start with true
statements and use valid reasoning steps, you can guarantee the
conclusion will also be true.
(It's like following a recipe.)
Deductive Logic: Conclusion necessarily follows from premises.
WHAT DOES THIS MEAN?

DEDUCTIVE LOGIC
Deductive Logic: Conclusion necessarily follows from premises.
If the premises (the initial statements or assumptions) are true, and if the
logical structure of the argument is valid, then the conclusion must also be
true.
This principle is known as the principle of deductive validity.

DEDUCTIVE LOGIC
All mammals are warm-blooded. (True premise)
EXAMPLE:
A dog is a mammal. (True premise)
Therefore, a dog is warm-blooded.

DEDUCTIVE LOGIC
SCENARIO:
Premise 1: The diamond necklace was last seen in the jewelry box.
Premise 2: The jewelry box was found in the locked safe.
Premise 3: Only the butler and the maid have access to the safe.
Premise 4: The butler has an alibi for the time when the necklace went
missing.
Conclusion: Therefore, based on deductive reasoning, the maid must have
taken the necklace.
Let's consider a detective solving a mystery using deductive logic:

INDUCTIVE LOGIC
• Inductive logic is a form of reasoning where conclusions
are drawn based on observed patterns.
• Inductive logic is like making an educated guess based on
what you've seen before. It's when you use past
experiences to make predictions about what might
happen next.
• Reasoning from specific
instances.

INDUCTIVE LOGIC
Explanation: Imagine you have a bag of colored marbles, and
you've pulled out ten marbles so far. All ten have been red.
Using inductive logic, you might guess that the next marble
you pull out will also be ___. Why?

INDUCTIVE LOGIC
Explanation: Imagine you have a bag of colored marbles, and
you've pulled out ten marbles so far. All ten have been red.
Using inductive logic, you might guess that the next marble
you pull out will also be ___. Why? Because based on the
pattern you've observed so far, it seems likely.

INDUCTIVE LOGIC
Example: Let's say you're a kid who loves ice cream. Every
time you go to the ice cream shop, you notice that they have
vanilla, chocolate, and strawberry flavors. Every time you've
gone, you've picked chocolate.
Using inductive logic, you might think that?

INDUCTIVE LOGIC
Example: Let's say you're a kid who loves ice cream. Every
time you go to the ice cream shop, you notice that they have
vanilla, chocolate, and strawberry flavors. Every time you've
gone, you've picked chocolate.
(Using inductive logic, you might think that?)
"Every time I've been to the ice cream shop, they've had
chocolate. So next time I go, they'll probably have chocolate
again." Based on your past experiences (inductive reasoning),
you make a prediction about the future.

INDUCTIVE LOGIC
Scenario: You've noticed that every time it rains, the streets
get wet. So, when you wake up one morning and see dark
clouds outside, you might use inductive logic to predict that
it will rain today. It's not guaranteed, but based on your past
observations, it seems likely.

SYMBOLIC LOGIC
Symbolic Logic: Using symbols to represent logical
relationships.
Symbolic logic is like using a secret code to talk about ideas.
Instead of using regular words and sentences, we use
symbols to represent different parts of logical statements,
like "and," "or," "not," and "if...then."
Deals with representing logical relationships and operations
using symbols.

SYMBOLIC LOGIC
Symbolic logic is like using a secret code to talk about ideas.
Instead of using regular words and sentences, we use
symbols to represent different parts of logical statements,
like "and," "or," "not," and "if...then."

SYMBOL MEANING
P It is raining.
Q I am using an umbrella.
∧ Conjunction (AND)
∨
Disjunction
(OR)
¬
Negation
(NOT)
→ Implication (IF...THEN)
↔
Equivalence (IF AND
ONLY IF)
SYMBOLIC LOGIC
1.) P∧Q
Represents "It is raining AND I am using an umbrella."

SYMBOL MEANING
P It is raining.
∨
Disjunction
(OR)
¬
Negation
(NOT)
→ Implication (IF...THEN)
↔
Equivalence (IF AND
ONLY IF)
SYMBOLIC LOGIC
1.) P∧Q
2.) ¬P
Represents "It is NOT raining."

SYMBOL MEANING
P It is raining.
∨
Disjunction
(OR)
¬
Negation
(NOT)
→ Implication (THEN)
↔
Equivalence (IF AND
ONLY IF)
SYMBOLIC LOGIC
1.) P∧Q
2.) ¬P
3.) (P→Q) ∧ (¬Q→¬P)
4.) (¬P∧¬Q)∨(P∧Q)
5.) (P∧Q)↔(Q∧P)

SYMBOL MEANING
P It is raining.
∨
Disjunction
(OR)
¬
Negation
(NOT)
↔
Equivalence (IF AND
ONLY IF)
SYMBOLIC LOGIC
1.) P∧Q
2.) ¬P
3.) (P→Q) ∧ (¬Q→¬P)
"If it is raining, then I am using an umbrella, and if I am not
using an umbrella, then it is not raining."

SYMBOL MEANING
P It is raining.
∨
Disjunction
(OR)
¬
Negation
(NOT)
↔
Equivalence (IF AND
ONLY IF)
SYMBOLIC LOGIC
1.) P∧Q
2.) ¬P
3.) (P→Q) ∧ (¬Q→¬P)
4.) (¬P∧¬Q)∨(P∧Q)

SYMBOL MEANING
P It is raining.
∨
Disjunction
(OR)
¬
Negation
(NOT)
↔
Equivalence (IF AND
ONLY IF)
SYMBOLIC LOGIC
1.) P∧Q
2.) ¬P
3.) (P→Q) ∧ (¬Q→¬P)
4.) (¬P∧¬Q)∨(P∧Q)
"It is not raining and I am not using an umbrella, or it is
raining and I am using an umbrella."

SYMBOL MEANING
P It is raining.
∨
Disjunction
(OR)
¬
Negation
(NOT)
↔
Equivalence (IF AND
ONLY IF)
SYMBOLIC LOGIC
1.) P∧Q
2.) ¬P
3.) (P→Q) ∧ (¬Q→¬P)
4.) (¬P∧¬Q)∨(P∧Q)
"It is not raining and I am not using an umbrella, or it is
raining and I am using an umbrella."
5.) (P∧Q)↔(Q∧P)
"It is raining and I am using an umbrella if and only if I am
using an umbrella and it is raining."

LOGIC & TRUTH.pptx PROPOSITIONAL LOGIC AND ETC.

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