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Prove that A is a subset of null set implies A = null set

Posted by Prabhjot Kaur Bamrah 3 years, 11 months ago

CBSE > Class 11 > Mathematics

1 answers

Ashutosh Agnihotri 3 years, 11 months ago

1. A is a member of the null set. (Given) 2. The null set has no members (By definition) 3. A is not a member of the null set. (Universal instantiation from (2)) 4. A is a member of the null set, or A is the null set (Disjunction Introduction from 1) 5. A is the null set (Disjunctive Syllogism, from 3, 4) It's not quite what you asked, but if you are not given that A is a member of the null set, you can still prove: 6. If A is a member of the null set, then A is the null set (Conditional proof, from 1, 5)

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CBSE > Class 11 > Mathematics