Exclusive and Inclusive Or Exclusive : only one of the two Inclusive : Both or one of the two An ice cream or Gulab jamun is available with a Thali in a restaurant . A student who has taken Physics or Maths can apply for Scholarship .
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 for p .
Implications : “ if and only if ” If and only if is bidirectional :