Logical Operations
Negation
Negation means the opposite of the original statement. If p is the statement, then the negation of p will be denoted by ~p and read as “It is not the case that p”. So if p is true then ~p will be false and vice versa.
Example – If the statement p is “New Delhi is in India”, then ~p will be “New Delhi is not in India”.
| p | ~p |
| T | F |
| F | T |
Conjunction
Conjunction means adding two statements. If p, q are two statements, then “p and q” is a compound statement then It will be denoted by p ∧ q and referred to as the conjunction of p and q.
The conjunction of p and q will be true only if p and q both are true otherwise p and q will be false.
| p | q | p ∧ q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Disjunction
Disjunction means oring of two statements. If p, q are two statements, then “p and q” is a compound statement. It is denoted by p V q and referred to as the disjunction of p and q. The disjunction of p and q is true whenever at least one of the two statements is true and if both statements are false then it will be false.
| p | q | p V q |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
Implication or If…then (⟶)
An implication of p ⟶ q is the proposition “if p, then q.” It is false if p is true and q is false. The rest cases are true.
| p | q | p ⟶ q |
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | F |
If And Only If (↔)
p ↔ q is a bi conditional logical connective so if the p and q both are the same for example p and q both are true or p and q both are false then it will be true otherwise it will be false.
| p | q | p ↔ q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | T |
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