Solution to Write Inverse, Converse and Contrapositive, also apply implication law on the following statements: a)If it … - Sikademy
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Write Inverse, Converse and Contrapositive, also apply implication law on the following statements: a)If it snows today. I will ski tomorrow.b)I come to class whenever there is going to be a quiz.c)I go to the beach whenever it is a sunny summer day.d) When I stay late, it is necessary that I sleep until noon.

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\text{if implication: } p\to q

\text{then }

\text{inverse: }\neg p\to \neg q

\text{converse: }q\to p

\text{contrapositive:}\neg q\to \neg p


\text{a)If it snows today. I will ski tomorrow.}

p:\text{ it snows today. }

q:\text{I will ski tomorrow.}

\neg p:\text{ it's not snowing today. }

\neg q:\text{ I won't ski tomorrow. }

\text{inverse: }\neg p\to \neg q

\text{If it's not snowing today. I won't ski tomorrow. }

\text{converse: }q\to p

\text{if I will ski tomorrow.Then it snows today.}

\text{contrapositive:}\neg q\to \neg p\text{ if I won't ski tomorrow.Then it's not snowing today }


\text{b)I come to class whenever there is going to be a quiz.}

\text{If there is a quiz.I come to class.}

p: \text{There is a quiz}

q:\text{I come to class.}

\neg p:\text{The quiz is not going}

\neg q:\text{I don't come to class.}

\text{inverse: }\neg p\to \neg q

\text{If the quiz is not going.I don't come to class.}

\text{converse: }q\to p

\text{If I come to class.The quiz is going}

\text{contrapositive:}\neg q\to \neg p

\text{If i don't come to class.The quiz is not going.}


\text{c)I go to the beach whenever it is a sunny summer day.}

\text{If it is a sunny summer day.I go to the beach.}

p: \text{it is a sunny summer day.}

q: \text{I go to the beach.}

\neg p :\text{it's not a sunny summer day now.}

\neg q :\text{I don't go to the beach.}

\text{inverse: }\neg p\to \neg q

\text{If it's not a sunny summer day now.I don't go to the beach.}

\text{converse: }q\to p

\text{If i go to the beach. It is a sunny summer day.}

\text{contrapositive:}\neg q\to \neg p

\text{If i don't go to the beach.It's not a sunny summer day now.}


\text{d) When I stay late, it is necessary that I sleep until noon.}

p:\text{I stay late.}

q:\text{ I sleep until noon.}

\neg p:\text{I don't stay late}

\neg q:\text{I don't sleep until noon.}

\text{inverse: }\neg p\to \neg q

\text{If i don't stay late.I don't sleep until noon.}

\text{converse: }q\to p

\text{ If i sleep until noon.I stay late.}

\text{contrapositive:}\neg q\to \neg p

\text{If i don't sleep until noon.I don't stay late}


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Question ID: mtid-5-stid-8-sqid-2797-qpid-1354