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Example 20 - Mathematical Reasoning
Last updated at Dec. 16, 2024 by Teachoo
Necessary and sufficient condition
Mathematical Reasoning
Concept wise
- Statements
- Writing negation of statements
- Negation - Checking if true or not
- Finding Compound Statement
- Words 'And' & 'Or'
- Inclusive and exclusive or
- Quantifiers
- Contrapositive and converse
- If then
- If and only if
- Proving not true/false (by giving counter examples)
- Proving True - If and only if
- Proving True - By Contrapositive
- Proving True - By Contradiction
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Necessary and sufficient condition
Transcript
Example 20 For the given statements identify the necessary and sufficient conditions. t: If you drive over 80 km per hour, then you will get a fine. Let p and q denote the statements: p : You drive over 80 km per hour. q : You will get a fine. If p then q means p is sufficient far q. That driving over 80 km per hour is sufficient to get a fine. Hence sufficient condition is driving over 80 km per hour If p then q means q is necessary for p When you drive over 80 km per hour , you will necessary get a fine Here the necessary condition is getting a fine
