第 11 类 RD Sharma 解决方案 – 第 31 章导数 – 练习 31.3
问题 1. 找出下列复合语句的组成语句：
（一）天是蓝的，草是绿的。
(ii) 地球是圆的，或者太阳是冷的。
(iii) 所有有理数都是实数，所有实数都是复数。
(iv) 25 是 5 和 8 的倍数。
解决方案：
每个复合语句都有组件。
(i) The component’s of the statement are:
A: The sky is blue.
B: The grass is green.
(ii) The component’s of the statement are:
A: The earth is round.
B: The sun is cold.
(iii) The component’s statement are:
A: All rational number are real.
B: All real number are complex.
(iv) The component’s of the statement are:
A: 25 is multiple of 5.
B: 25 is multiple of 8.
问题 2. 对于以下每个陈述，确定是否使用了包含性“或”或排除性“或”。解释你的回答。
(i) 学生可以将印地语或梵语作为第三语言。
(ii) 要进入一个国家，您需要护照或选民登记卡。
(iii) 一位女士生下男婴或女婴。
(iv) 要申请驾驶执照，您应该有配给卡或护照。
解决方案：
(i) A choice is given to a student to choose either Hindi or Sanskrit as their third language. The student can’t choose both. Therefore, an exclusive “OR” is used because a student cannot take both Hindi and Sanskrit.
(ii) A passport or voter registration card is needed by a person to enter a country. However, a person may have both. Therefore, an inclusive “OR” is used because a person can have both a passport and a voter registration card to enter a country.
(iii) A lady cannot give birth to a baby who is both a boy and a girl, therefore, an exclusive “OR” is used because either a boy or girl is born.
(iv) A ration card or passport is needed to apply a driving license. However, a person may have both.Therefore, an inclusive “OR” is used because a person can have both a ration card and passport to apply for a driving license.
问题 3. 写出下列复合语句的组成语句，并检查复合语句的真假：
(i) 儿童进入公共图书馆需要学校的身份证或学校当局的信。
(ii) 所有有理数都是实数，所有实数都不是复数。
(iii) 整数的平方是正的还是负的。
(iv) x = 2 和 x = 3 是方程 3x 2 – x – 10 = 0 的根。
(v) 沙子在阳光下迅速升温，而在夜间不会迅速降温。
解决方案：
(i) The components are:
P: To get into a public library children need an identity card from the school.
Q: To get into a public library children need a letter from the school authorities.
Both of the statements P and Q are true. Therefore, the compound statement is true.
(ii) The components are:
P: All rational numbers are real.
Q: All real numbers are not complex.
The statement P is true and Q is false therefore, P and Q both together are False. Therefore, the compound statement is False
(iii) The components are:
P: Square of an integer is positive.
Q: Square of an integer is negative.
Both statements P and Q are true. Therefore, the compound statement is True.
(iv) The components of the compound statement are:
P: x = 2 is a root of the equation 3x2 – x – 10 = 0
Q: x = 3 is a root of the equation 3x2 – x – 10 = 0
The statement P is true, but Q is false then P and Q both combined are False. Therefore, the compound statement is False.
(v) The components of the compound statement are:
P: The sand heats up quickly in the sun.
Q: The sand does not cool down fast at night.
Both statements P and Q both are False. Therefore, the compound statement is False.
问题 4. 确定以下复合陈述是对还是错：
(i) 德里在印度，2 + 2 = 4
(ii) 德里在英格兰，2 + 2 = 4
(iii) 德里在印度，2 + 2 = 5
(iv) 德里在英格兰，2 + 2 = 5
解决方案：
(i) The components are:
A: Delhi is in India.
B: 2 + 2 = 4
Both statements A and B are true. Hence, the compound statement is True.
(ii) The components are:
A: Delhi is in England.
B: 2 + 2 = 4
The statement A is false, and B is true. So, both A and B together are false. Hence, the compound statement is False.
(iii) The components are:
A: Delhi is in India.
B: 2 + 2 = 5
The statement B is false, and A is true. So, both A and B together are false. Hence, the compound statement is False.
(iv) The components are:
A: Delhi is in England.
B: 2 + 2 = 5
Both the statements A and B are false. Hence, the compound statement is False.