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Consider these statements: p: The weather is not cloudy; q: It is not going to rain. If p => q, which of the following is a valid conclusion?
Mathematics
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Step-by-step solution
3 stepsIdentify the given statements and the implication.
The given statements are:
: The weather is not cloudy.
: It is not going to rain.
The implication is , which means "If the weather is not cloudy, then it is not going to rain."Determine the negations of the statements.
The negation of is : The weather is cloudy.
The negation of is : It is going to rain.Apply the rule of contrapositive.
A valid conclusion from an implication is its contrapositive, which is .
Substituting the statements:
means "If it is going to rain, then the weather is cloudy."A valid conclusion is:
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