问题1.以“ if p，then q”的形式写以下每个语句。
(i)仅在您支付订阅费后才能访问该网站。
(ii)下雨时交通堵塞。
(iii)必须具有护照才能登录到服务器。
(iv)有必要为了快乐而变得富有。
(v)游戏只有在下雨的时候才被取消。
(vi)只有在寒冷的时候才下雨。
(vii)每当下雨，就很冷。
(viii)天冷时从不下雨。
解决方案：
(i) If you pay a subscription fee, then you can access the website .
(ii) If it rains, then there is a traffic jam.
(iii) If you log on the server, then you must have a passport.
(iv) If he is happy, then he is rich.
(v) If it is raining, then the game is canceled.
(vi) If it rains, then it is cold.
(vii) If it rains, then it is cold.
(viii) If it is cold, then it never rains.
问题2.陈述以下各陈述的相反和对立：
(i)如果外面很热，那么您会感到口渴。
(ii)每当晴天，我都会去海滩。
(iii)一个正整数只有在除1和自身以外没有除数的情况下才是质数。
(iv)如果您住在德里，那您就穿冬衣。
(v)如果四边形是平行四边形，则其对角线将一分为二。
解决方案：
(i) If it is hot outside, then you feel thirsty.
The converse and contrapositive are as follows :
Converse: If you feel thirsty, then it is hot outside.
Contrapositive: If you do not feel thirsty, then it is not hot outside.
(ii) I go to a beach whenever it is a sunny day.
The converse and contrapositive are as follows :
Converse: If I go to a beach, then it is a sunny day.
Contrapositive: If I do not go to a beach, then it is not a sunny day.
(iii) A positive integer is prime only if it has no divisions other than 1 and itself.
The converse and contrapositive are as follows :
Converse: If an integer has no divisor other that 1 and itself, then it is prime.
Contrapositive: If an integer has some divisor other than 1 and itself, then it is prime.
(iv) If you live in Delhi, then you have winter clothes.
The converse and contrapositive are as follows :
Converse: If you have winter clothes, then you live in Delhi.
Contrapositive: If you do not have winter clothes, then you do not live in Delhi.
(v) If a quadrilateral is a parallelogram, then its diagonals bisect each other.
The converse and contrapositive are as follows :
Converse: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Contrapositive: If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.
问题3.以“ p if and only is q”的形式重写以下每个语句。
(i)p：如果您看电视，那么您的思想是自由的；如果您看电视，则您的思想是自由的。
(ii)q：如果四边形是等角的，那么它是一个矩形，如果四边形是矩形的，那么它是等角的。
(iii)r：要获得A级成绩，有必要并定期进行所有家庭作业。
(iv)s：如果一个漱口杯一半是空的，那么它是半满的；如果一个漱口杯一半是半满的，那么它是半空的。
解决方案：
(i) You watch television if and only if your mind is free.
(ii) A quadrilateral is a rectangle if and only if it is equiangular.
(iii) You get an A grade if and only if you do all the homework regularly.
(iv) A tumbler is half empty if and only if it is half full.
问题4.确定以下每个陈述的对立面：
(i)如果莫汉是诗人，那么他就是穷人。
(ii)只有通过Max学习，他才能通过考试。
(iii)如果她工作，她将赚钱。
(iv)如果下雪了，那么他们就不会开车。
(v)天冷时从不下雨。
(vi)如果拉维什(Ravish)滑雪，那就下雪了。
(vii)如果x小于零，则x不为正。
(viii)如果他有勇气，他将获胜。
(ix)必须坚强才能成为水手。
(x)只有他不疲倦，他才能获胜。
(xi)如果x是整数并且x2是奇数，则x是奇数。
解决方案：
(i) If Mohan is a poet, then he is poor.
The contrapositive is as follows :
Contrapositive: If Mohan is not poor, then he is not a poet.
(ii) Only if Max studies will he pass the test.
The contrapositive is as follows :
Contrapositive: If Max does not study, then he will not pass the test.
(iii) If she works, she will earn money.
The contrapositive is as follows :
Contrapositive: If she does not earn money, then she does not work.
(iv) If it snows, then they do not drive the car.
The contrapositive is as follows :
Contrapositive: If then they do not drive the car, then there is no snow.
(v) It never rains when it is cold.
The contrapositive is as follows:
Contrapositive: If it rains, then it is not cold.
(vi) If Ravish skis, then it snowed.
The contrapositive is as follows :
Contrapositive: If it did not snow, then Ravish will not ski.
(vii) If x is less than zero, then x is not positive.
The contrapositive is as follows:
Contrapositive: If x is positive, then x is not less than zero.
(viii) If he has courage he will win.
The contrapositive is as follows :
Contrapositive: If he does not win, then he does not have courage.
(ix) It is necessary to be strong in order to be a sailor.
The contrapositive is as follows :
Contrapositive: If he is not strong, then he is not a sailor
(x) Only if he does not tire will he win.
The contrapositive is as follows :
Contrapositive: If he tries, then he will not win.
(xi) If x is an integer and x2 is odd, then x is odd.
The contrapositive is as follows :
Contrapositive: If x is even, then x2 is even.