Confused with sufficient and necessary condition

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The discussion centers on the distinction between necessary and sufficient conditions in logic. It clarifies that "A is necessary for B" means that if B is true, then A must also be true, which is expressed as "B implies A." However, confusion arises with the phrase "A is necessary of B," which is not a standard expression in logical terminology. Participants seek clarification on the correct usage and implications of these terms. Understanding these concepts is crucial for accurately interpreting logical statements.
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Homework Statement




i know that "A is necessary for B" means "B implies A".

but i confused with the word "A is necessary of B" somebody help
 
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annoymage said:

Homework Statement




i know that "A is necessary for B" means "B implies A".

but i confused with the word "A is necessary of B" somebody help
Take a look here.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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