问题1.写以下语句的否定：
(i)钦奈是泰米尔纳德邦的首都。
The negation of the statement is
Chennai is not the capital of Tamil Nadu.
Or
It is false that chennai is the capital of Tamil Nadu.
(ii)√2不是复数
The negation of the statement is
√2 is a complex number
Or
It is false that √2 is not a complex number
(iii)所有三角形都不是等边三角形。
The negation of the statement is
All triangles are equilateral triangle.
Or
It is false that all triangles are not equilateral triangle.
(iv)数字2大于7。
The negation of the statement is
The number 2 is not greater than 7.
Or
It is false that the number 2 is greater than 7.
(v)每个自然数都是整数。
The negation of the statement is
Every natural number is not an integer.
Or
It is false that every natural number is an integer.
问题2。以下几对语句彼此否定：
(i)x不是有理数。
数字x不是无理数。
Yes, they both are the negation of each other because negation of first statement is
The number x is a rational number.
which means that x is not an irrational number so the negation can also be written as
The number x is not an irrational number
Note: There are two types of number rational number and irrational number. If a number is not rational it will be irrational and vice-versa.
(ii)数字x是一个有理数。
x是无理数。
Yes, they both are the negation of each other because the negation of the first statement is
The number x is not a rational number.
which means that x is an irrational number so the negation can also be written as
The number x is an irrational number
问题3.查找以下复合语句的component语句，并检查它们是对还是错。
(i)3是素数或奇数。
The component statements are
p: Number 3 is prime
q: Number 3 is odd
Here the connecting word is or therefore we know that if anyone the statement is true than whole statement will be true.
We know that 3 is both prime as well as odd number
p -> TRUE
q -> TRUE
Hence, the statement is TRUE.
(ii)所有整数都是正数或负数。
The component statements are
p: All integers are positive
q: All integers are negative
Here the connecting word is Or therefore we know that the statement will only be FALSE if both statement are false.
we also know that 0 is neither positive nor negative.
p -> FALSE
q -> FALSE
Hence, the statement is FALSE.
(iii)100被3、11和5整除。
The component statements are
p: 100 is divisible by 3
q: 100 is divisible by 11
r: 100 is divisible by 5
Here the connecting word is AND therefore we know that the statement will be FALSE if any of the statement is false.
we also know that 100 is not divisible by 3 and 11 but it is divisible by 5.
p -> FALSE
q -> FALSE
r -> TRUE
Hence, the statement is FALSE.