Question

Translate the following statements into propositional logic: "Whenever it is raining, I do not walk the dog. If I walk the dog, then I get exercise. If I do not get exercise, then it is not raining." Use the propositional variables r, w, e; clearly state what each propositional variable stands for. 1. ' r ' stand for ' it is raining ' 2. ' w ' stand for ' I walk the dog ' 3. ' e ' stand for ' I get exercise ' (r => ~w) ^ (w => e) ^ (~e => ~r) A consistent set of statements does not contain any contradictions. Are the statements in the previous part consistent? If so, give an assignment of truth values to propositions such that the statement set evaluates to True; if not, use logical equivalences to show the contradiction. * No, the statement in the previous part is not consistent.

          Translate the following statements into propositional logic:

"Whenever it is raining, I do not walk the dog. If I walk the dog, then I get exercise. If I do not get exercise, then it is not raining."

Use the propositional variables r, w, e; clearly state what each propositional variable stands for.

1. ' r ' stand for ' it is raining '
2. ' w ' stand for ' I walk the dog '
3. ' e ' stand for ' I get exercise '

(r => ~w) ^ (w => e) ^ (~e => ~r)

A consistent set of statements does not contain any contradictions. Are the statements in the previous part consistent? If so, give an assignment of truth values to propositions such that the statement set evaluates to True; if not, use logical equivalences to show the contradiction.

* No, the statement in the previous part is not consistent.

Translate the following statements into propositional logic:

"Whenever it is raining, I do not walk the dog. If I walk the dog, then I get exercise. If I do not get exercise, then it is not raining."

Use the propositional variables r, w, e; clearly state what each propositional variable stands for.

1. ' r ' stand for ' it is raining '
2. ' w ' stand for ' I walk the dog '
3. ' e ' stand for ' I get exercise '

(r => w) ^ (w => e) ^ ( e => r)

A consistent set of statements does not contain any contradictions. Are the statements in the previous part consistent? If so, give an assignment of truth values to propositions such that the statement set evaluates to True; if not, use logical equivalences to show the contradiction.

* No, the statement in the previous part is not consistent.

Added by Nichole H.

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