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@Deyse SJ de Assis - Lisboa, Portugal

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LOGICAL REASONING >>

Logical Propositions

What are they?

They are sentences that can have only two values:

✅ True (T)

❌ False (F)

There is no “more or less true”

Examples of propositions:

“2 + 2 = 4” → True

“Lisbon is in Brazil” → False

“10 is greater than 5” → True

What is NOT a proposition

Sentences that cannot be judged as true or false:

❓ Questions → “What time is it?”

📢 Commands → “Close the door”

😮 Exclamations → “What a beautiful day!”

These do NOT belong to logic

Types of propositions

Simple proposition

A single idea:

“It is raining”

“John studies”

Compound proposition

Combination of two or more ideas:

“It is raining and it is cold”

“John studies or works”

Every proposition must:

Be a declarative sentence

Have complete meaning

Be classified as T or F

⚠️ Common trap

Sentence:

“x + 2 = 5”

This is not a proposition because it depends on the value of x.

Quick summary

Proposition = sentence with a logical value (T or F)

Cannot be a question, command, or emotion

Can be simple or compound

It is the foundation of all Logic

Did you know?

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👉 Example:
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📌 Example: tossing a coin twice
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General Rule
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(2,5)
(3,4)
(4,3)
(5,2)
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📌 Example
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\( P(A \cap B) = P(A) \times P(B)
📌 Example
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\( P(\text{heads}) = \frac{1}{2}
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