问题1.用五种表示相同含义的不同方式，用“ if-then”重写以下语句。
如果自然数为奇数，则其平方也为奇数。
解决方案：
(i) An odd natural number implies that its square is odd.
(ii) If a natural number is odd it means that its square is also odd.
(iii) A natural number is odd only if its square is odd.
(iv) If the square of a natural number is not odd, then the natural number is not odd.
(v) For the square of a natural number to be odd, the natural number should be odd.
问题2：写下以下陈述的相反和相反。
(i)如果x是质数，则x是奇数。
(ii)如果两条线是平行的，则它们不在同一平面上相交。
(iii)较冷的事物表示温度较低。
(iv)如果您不知道如何演绎推理，则无法理解几何。
(v)x为偶数表示x可被4整除
解决方案：
(i) Contrapositive:
If a number x is not odd, then x is not a prime number.
Converse:
If a number x is odd, then it is a prime number
(ii) Contrapositive:
If two lines intersect in the same plane, then the two lines are not parallel.
Converse:
If two lines do not intersect in the same plane, then they are parallel
(iii) Contrapositive:
If something does not have low temperature, then it is not cold.
Converse:
If something is at low temperature, then it is cold.
(iv) Contrapositive:
If you know how to reason deductively, then you can comprehend geometry.
Converse:
If you do not know how to reason deductively, then you cannot comprehend geometry.
(v) Contrapositive:
If x is not divisible by 4, then x is not an even number.
Converse:
If x is divisible by 4, then x is an even number.
问题3.以“ if-then”的形式编写以下每个语句。
(i)您找到工作意味着您的资历良好。
(ii)如果香蕉树保暖一个月，它将开花。
(iii)如果一个四边形的对角线一分为二，则它是一个平行四边形。
(iv)要获得班上的A +，有必要做这本书的练习。
解决方案：
(i)To get a job you should have good credentials
(ii) For the banana trees to bloom, it should stay warm for a month.
(iii) For a quadrilateral to be a parallelogram, it’s diagonals should bisect each other.
(iv) If you do not do all exercises of the book, then you would not get an A+ in the class.
问题4.(a)和(b)中给出的陈述。确认以下给出的陈述是相反的或相反的。
(a)如果您住在德里，那么您就穿冬衣。
(i)如果您没有冬装，那么您就不会住在德里。
(ii)如果您有冬装，那么您住在德里。
(b)如果四边形是平行四边形，则其对角线将一分为二。
(i)如果四边形的对角线不一分为二，则该四边形不是平行四边形。
(ii)如果四边形的对角线一分为二，则为平行四边形。
解决方案：
(a) (i) Contrapositive
(ii) Converse
(b) (i) Contrapositive
(ii) Converse