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Negation

Which of the ...

Question

Which of the following statements is the inverse of "If you do not understand geometry, then you do not know how to reason deductively."?

If you reason deductively, then you understand geometry.

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If you understand geometry, then you reason deductively.

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If the do not reason deductively, then you understand geometry.

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None of these

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Solution

The correct option is A If you reason deductively, then you understand geometry.
To find the inverse we need to negate the hypothesis and conclusion.On negating the hypothesis we get you reason deductively and on negating the conclusion we get you understand geometry.

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Similar questions

Write the contrapositive and converse of the following statements.

(i) If x is a prime number, then x is odd.

(ii) If the two lines are parallel, then they do not intersect in the same plane.

(iii) Something is cold implies that it has low temperature.

(iv) You cannot comprehend geometry if you do not know how to reason deductively.

(v) x is an even number implies that x is divisible by 4.

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x

x

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4

Write the converse and contrapositive of each of the following statements:

(i) If n is an even number, then $n^{2}$ is even.

(ii) If two integers a and b are such that $a > b,$ then $(a - b)$ is always a positive integer.

(iii) If a $Δ A B C$ is right angled at B, then $A B^{2} + B C^{2} = A C^{2} .$

(iv) If $Δ A B C$ and $Δ D E F$ are congruent, then they are equiangular.

(v) You cannot comprehend geometry if you do not know how to reason deductively.

(vi) Something is cold implies that it has low temperature.

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