Logic / Truth Tables
Least You Need to Know: Truth Tables and Equivalence
Truth tables let you compare two statements **row by row**. Two statements are logically equivalent when they match on **every** row.
جو کم از کم جاننا ضروری ہے
- A truth table checks every possible truth assignment.
- If two columns match in every row, the statements are equivalent.
- An implication is false only when the premise is true and the conclusion is false.
- A tautology is always true; a contradiction is always false.
- Equivalence is about matching truth values, not just sounding similar.
اہم علامتیں
¬p
not p
p ∧ q
p and q
p ∨ q
p or q
p → q
if p then q
p ↔ q
p if and only if q
مختصر حل شدہ مثال
- Compare `p → q` with `¬p ∨ q`.
- In every row of the truth table, these columns match.
- So `p → q` and `¬p ∨ q` are logically equivalent.
عام غلطیاں
- Students often think one matching row is enough for equivalence.
- Students often forget the special false row for implication.
- Students often confuse `↔` with `→`.
اس قسم کے سوال کو کیسے پہچانیں
- The prompt asks whether two statements are equivalent.
- You are asked whether a statement is a tautology or contradiction.
- The problem mentions all possible truth values or rows.
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