问题1.以下哪句话是陈述?解释你的回答?
Note: A sentence is called mathematically acceptable statement if it is either true or false but not both.
(i)一个月中有35天。
解决方案：
Yes, this is a stament because there can be 28 / 29 / 30 / 31 days in a month but not 35 and therefore this is definitely false.
(ii)数学很难。
解决方案：
No, this is not a stament because for some people math can be easy and for some it is difficult. so it can be both true and false in.
(iii)5和7之和大于10。
解决方案：
Yes, this is a stament because 5 + 7 = 12, which is greater than 10 and therefore this is definitely true.
(iv)数字的平方是偶数。
解决方案：
No, this is not a stament because square of 3 is 9 which is odd and square of 4 is 16 which is even. so it can be both true and false.
(v)四边形的边长相等。
解决方案：
No , this is not a stament because square is a quadrilateral which has all sides equal but for rectangle which is also a quadrilateral in which all sides are not eual. so it can be both true and false.
(vi)回答这个问题。
解决方案：
No, this is not a statement because this an order and we cannot say whether it is true or false.
(vii)(–1)与8的乘积为8。
解决方案：
Yes , this is a stament because product of -1 and 8 is -8 and therefore this is definitely false.
(viii)三角形的所有内角之和为180°。
解决方案：
Yes, this is a statement because sum of all interior triangle is 180° in a triangle and therefore this is definitely true.
(ix)今天是大风天。
解决方案：
No, this is not a statement because a day can be either windy or not windy we cannot say whether it is true or false.
(x)所有实数均为复数。
解决方案：
Yes , this is a statement because all real numbers are complex with imaginary part as 0 and therefore this is definitely true.
问题2。给出三个不是语句的句子示例。请给出答案的原因?
解决方案：
- How far is Chennai from here? This is a question which also contains the word “Here”. Hence it is not a statement
- Tomorrow is Friday. This sentece can either be true or false hence it is not a statement.
- The sum of x and y is greater than 0 .Here, we are not in a position to determine whether it is true or false, unless we know what x and y are and therefore this is not a statement.