Logical Connectives
What are they?
They are words that connect propositions (logical sentences).
Main connectives
AND (∧)
everything must be true
Example:
“A is true AND B is true” → ✅ True
If one is false → ❌ False
OR (∨)
at least one must be true
Example:
“A is true OR B is false” → ✅ True
Only false if both are false
IF... THEN (→)
Indicates a condition:
“If A happens, then B happens”
👉 Only false when:
A = True and B = False
IF AND ONLY IF (↔)
Both must have the same value:
✅ True if both are true or both are false
❌ False if they are different
⚠️ Important tip (very common)
👉 The “OR” in logic is inclusive
That means both can be true as well
Quick summary
AND → everything true
OR → at least one true
IF... THEN → fails in only 1 case
IF AND ONLY IF → same values
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