Class 11 Maths Mathematical Reasoning Implications

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: 

  • Both are true or false together
  • Both sufficient and necessary condition.

E.g. Krishna will eat if and only if food is Apple.

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