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Consider this statement "If the bank was robbed then I will not have any money".

Therefore, given $\textbf{p}$: "The bank was robbed" and $\textbf{q}$: "I will not have any money", which of the following are correct?

(1) The converse is $\sim p \rightarrow q$

(2) The inverse is $\sim q \rightarrow p$

(3) The contrapositive is $q \rightarrow \sim p$

(A) (1), (2) and (3) are all incorrect (B) (1) and (2) are correct, (3) is incorrect (C) (1), (2) and (3) are all correct (D) Only (3) is correct
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Given this statement "If the bank was robbed then I will not have any money", where $\textbf{p}$: "The bank was robbed" and $\textbf{q}$: "I will not have any money",
The converse is "If I do not have money, then the bank was robbed" $\Rightarrow \sim q \rightarrow p$
The inverse is "If the bank was not robbed, then I have money" $\Rightarrow \sim q \rightarrow p$
The contrapositive is "If I have any money, then the bank was robbed" $\Rightarrow q \rightarrow \sim p$
Therefore (1) and (2) are incorrect and (3) is correct $\rightarrow$ (D) is the correct answer.
answered Mar 20, 2014 by balaji.thirumalai
 

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