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Understanding Necessary and Sufficient condition

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In this post, I will try to come up with examples from set theory as well as generic examples to help you understand necessity and sufficiency conditions better. Case 1 : A is both necessary and sufficient condition for B Set Theory example: Two identical sets A & B. If an element belongs to B it implies it belongs to A (so A is necessary for B) and if an element belongs to A it implies it belongs to B. (so A is sufficient for B) Generic Example: