2. Disjunction (OR)
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Table of Content:
⚡ Disjunction (OR)
In logic, Disjunction means OR.
It is written as:
👉 p ∨ q
(or sometimes p + q)
Read as: "p OR q"
🧠 What does it mean?
A statement with OR is true if at least one part is true.
Think of this:
“You can have ice cream if it’s Sunday OR your homework is done.”
That means:
-
If it’s Sunday → ✅ Ice cream!
-
If homework is done → ✅ Ice cream!
-
If both → ✅ Ice cream!
-
Only if both are false → ❌ No ice cream!
🔢 Truth Table for p ∨ q (Using 0 and 1)
| p | q | p ∨ q |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
📌 Summary:
| Situation | Result |
|---|---|
| Both false (0 + 0) | ❌ 0 |
| At least one true (1 + 0, 0 + 1, 1+1) | ✅ 1 |
🎉 Example:
-
p = It’s Sunday
-
q = Homework is done
-
p ∨ q = You get ice cream
Only if both are false (0, 0) → no ice cream.
Otherwise, 🍦 all the way!