问题1：对于以下每个复合语句，首先确定连接词，然后将其分解为组件语句。
(i)所有有理数都是实数，所有实数都不复杂。
解决方案：
Here, the connecting word is “and”.
Now, the component statements of this compound statement are –
(a) All rational numbers are real.
(b) All real numbers are not complex.
(ii)整数的平方为正或负。
解决方案：
Here, the connecting word is “or”.
Now, the component statements of this compound statement are –
(a) Square of an integer is positive.
(b) Square of an integer is negative.
(iii)沙子在阳光下迅速变热，而在夜间却不迅速冷却。
解决方案：
Here, the connecting word is “and”.
Now, the component statements of this compound statement are –
(a) The sand heats up quickly in the Sun.
(b) The sand does not cool down fast at night.
(iv) x = 2和x = 3是等式3x 2 – x – 10 = 0的根。
解决方案：
Here, the connecting word is “and”.
Now, the component statements of this compound statement are –
(a) x = 2 is the root of the equation 3x2 – x – 10 = 0.
(b) x = 3 is the root of the equation 3x2 – x – 10 = 0.
问题2：在以下语句中确定量词，并写出语句的否定词。
(i)存在一个等于其平方的数字。
解决方案：
Here, the quantifier is “There exists”.
Now, the negation of this statement will be: There does not exist a number which is equal to its square.
(ii)对于每个实数x，x小于x + 1。
解决方案：
Here, the quantifier is “For every”.
Now, the negation of this statement will be: For every real number x, x is not less than x + 1.
(iii)印度每个州都有一个首都。
解决方案：
Here, the quantifier is “There exists”.
Now, the negation of this statement will be: There exists a state in India which does not have a capital.
问题3：检查以下语句对是否彼此求反。解释你的回答。
(a)x + y = y + x对于每个实数x和y为真。
(b)存在x和y = y + x的实数x和y。
解决方案：
Answer: The given pair of statements are not negation of each other.
Reason:
To check if the given pair of statements are negation of each other, First of all we will find the negation of statement (a),
So, The negation of statement (a) : There exists real number x and y for which x + y ≠ y + x.
Since, The negation of statement (a) is not same as statement (b).
Thus, The given pair of statements are not negation of each other.
问题4：陈述以下陈述中使用的“或”是否为“排他性”或“含”性。解释你的回答。
(i)太阳升起或月亮落山。
解决方案：
Answer: The “Or” used in this statement is exclusive.
Reason:
We know that, It is not possible that Sun will rise and Moon will set together.
Since, It is not possible for both events to occur simultaneously.
Thus, The “Or” used in this statement is exclusive.
(ii)要申请驾驶执照，您应该有一张口粮卡或护照。
解决方案：
Answer: The “Or” used in this statement is inclusive.
Reason:
We know that, A person could have both a ration card and a passport to apply for a driving license.
Since, It is possible for both events to occur simultaneously.
Thus, The “Or” used in this statement is inclusive.
(iii)所有整数都是正数或负数。
解决方案：
Answer: The “Or” used in this statement is exclusive.
Reason:
We know that, A integer can not be both positive and negative.
Since, It is not possible for both events to occur simultaneously.
Thus, The “Or” used in this statement is exclusive.