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    2. Disjunction (OR)

    Rumman Ansari April 12, 2026 233 views

    ⚡ 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.

    It's meaning is either p is true, or q is true, or both.

    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!