Page 3 - LESSON NOTE
P. 3
Quantifiers
Quantifiers are phrases like, “There exists” and “For all”.
There exists a girl who is beautiful
For every prime number p, √p is an irrational number.
Implications : “if-then”, “only if”
If then: Sufficient condition
If food is Sandwich, then Rohit will eat food
If food is Burger, then Rohit will eat food
If food is Pizza, then Rohit will eat food
Only if: Necessary condition
Only if Rohit ate food, food is Sandwich.
Only if Rohit ate food, food is Burger.
Only if Rohit ate food, food is Pizza.
Sufficient is inverse of necessity. If (p à q), then p is sufficient condition for q and q is necessary
condition fo
Implications : “if and only if ”:
If and only if is bidirectional:
o Both are true or false together
o Both sufficient and necessary condition.
E.g. Krishna will eat if and only if food is Apple
Contrapositive, Converse, Inverse:
Statement: if p then q
Converse: if q then p
Inverse: if not p then not q
Contrapositive: if not q then not p
If a statement is true, contrapositive is also true.
