Consider the following statements:
A : Rishi is a judge.
B : Rishi is honest.
C : Rishi is not arrogant.
The negation of the statement “if Rishi is a judge and he is not arrogant, then he is honest” is
A : Rishi is a judge.
B : Rishi is honest.
C : Rishi is not arrogant.
The negation of the statement “if Rishi is a judge and he is not arrogant, then he is honest” is
- B → (A ∨ C)
- (~ B) ∧ (A ∧ C)
- B → ((~ A) ∨ (~ C))
- B → (A ∧ C)
The Correct Option is B
Solution and Explanation
The given statement is:
\((A ∧ C) → B\)
The negation of the statement is :
\(~ {(A ∧ C) → B}\) or \(~ {~ (A ∧ C) ∨ B}\)
\(∴ (A ∧ C) ∧ (~ B)\) or \((~ B) ∧ (A ∧ C)\)
Hence, the correct option is (B): (~ B) ∧ (A ∧ C)
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Concepts Used:
Logarithmic Differentiation
Logarithmic differentiation is a method to find the derivatives of some complicated functions, using logarithms. There are cases in which differentiating the logarithm of a given function is simpler as compared to differentiating the function itself. By the proper usage of properties of logarithms and chain rule finding, the derivatives become easy. This concept is applicable to nearly all the non-zero functions which are differentiable in nature.
Therefore, in calculus, the differentiation of some complex functions is done by taking logarithms and then the logarithmic derivative is utilized to solve such a function.