Put the following into logic symbolic form. Yossarian is crazy if he flies his m

Question

Put the following into logic symbolic form. Yossarian is crazy if he flies his missions. If he is crazy, he is not obligated to fly his missions. If Yossarian asks to be grounded then he is showing concern for his own safety in the face of real, immediate danger. However if he shows such concern then he is not crazy and is obligated to fly his missions. Moreover, Yossarian won’t fly his missions only if he both asks to be grounded and is not obligated to fly them. Therefore Yossarian is not obligated to fly his missions but flies them nonetheless. A = Yossarian is crazy. B = Yossarian flies his missions. C = Yossarian asks to be grounded. D = Yossarian shows concern for his own safety in the face of real immediate danger.

Explanation / Answer

A = Yossarian is crazy.
B = Yossarian flies his missions.
C = Yossarian asks to be grounded.
D = Yossarian shows concern for his own safety in the face of real immediate danger.
E = Yossarian is not obligated to fly his missions

B -> A               // Yossarian is crazy if he flies his missions
A -> ~E               // If he is crazy, he is not obligated to fly his missions
C -> D               // If Yossarian asks to be grounded then he is showing concern for his own safety in the face of real, immediate danger
D -> (~A . E)       // if he shows such concern then he is not crazy and is obligated to fly his missions
(C . ~E) -> ~B       // Yossarian won’t fly his missions only if he both asks to be grounded and is not obligated to fly them

~E . B               // Therefore Yossarian is not obligated to fly his missions but flies them nonetheless

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