NCERT Solution class 6 math Exercise 2.1 part:2
Question (8) Which of the following statements are true (T) and which are false (F)?
(a) Zero is the smallest natural number.
Answer False (F)
Explanation
Counting numbers are called natural numbers.
Thus, 1, 2, 3, 4, 5, . . . . are natural numbers.
Thus, 1 is the smallest natural number.
This means zero (0) does not come in the list of natural numbers.
Thus, the given statement, "Zero is the smallest natural number" is false (F).
(b) 400 is the predecessor of 399
Answer False (F)
Explanation
The number comes just before a number is called the predecessor of the given number.
This, means we can get a predecessor of a number by subtracting 1 to the given number.
Thus, predecessor of 399
= 399 – 1 = 398
Thus, 398 is the predecessor of 399.
Hence, the given statement "400 is the predecessor of 399" is false (F).
The correct statement is "400 is the successor of 399".
(c) Zero is the smallest whole number.
Answer True (T)
Explanation
The natural numbers along with zero (0) are called whole numbers.
Thus, 0, 1, 2, 3, 4, . . . . are whole numbers.
Here, zero (0) is the smallest whole number.
Thus, the given statements "Zero is the smallest whole number" is true (T).
(d) 600 is the successor of 599
Answer True (T)
Explanation
The number comes just after a given number is called the successor of a given number.
This, means we can get the successor of a given number by adding 1 to the given number.
Thus, successor of 599
= 599 + 1 = 600
Thus, the given statement "600 is the successor of 599" is true (T).
(e) All natural numbers are whole numbers.
Answer True (T)
Explanation
The natural numbers along with zero (0) are called whole numbers.
Thus, all natural numbers are whole numbers.
Thus, the given statement "All natural numbers are whole numbers" is true (T).
(f) All whole numbers are natural numbers.
Answer False (F)
Explanation
The natural numbers along with zero (0) are called whole numbers.
1, 2, 3, 4, 5, . . . . . . are natural numbers.
And, 0, 1, 2, 3, 4, 5, . . . . . . are whole numbers.
This means, zero (0) does not come in the list of natural numbers.
Thus, all natural numbers are whole numbers, but all whole numbers are not natural numbers.
Thus, the given statement "All whole numbers are natural numbers" is false (F).
(g) The predecessor of a two-digit number is never a single digit number.
Answer False (F).
Explanation
The number comes just before a number is called the predecessor of the given number.
This means, we can get the predecessor of a number by subtracting 1 from it.
Thus, the predecessor of 10 which is a two-digit number
= 10 – 1 = 9
Here, 9 is a single digit number.
And, 10 is a two-digit number.
And, here 9 is the predecessor of 10.
This means, 9 which is a single digit number is the predecessor of the two-digit number 10.
Thus, the given statement "The predecessor of a two-digit number is never a single digit number" is false (T).
(h) 1 is the smallest whole number.
Answer False (F).
The correct statement is 0 (zero) is the smallest whole number.
Explanation
Natural numbers along with zero (0) are called the Whole numbers.
This means, 0, 1, 2, 3, 4, . . . . are whole numbers.
Thus, zero (0) is the smallest whole number.
Thus, the given statement "1 is the smallest whole number" is false (F).
The correct statement is 0 (zero) is the smallest whole number.
And, 1 is the smallest natural number.
(i) The natural number 1 has no predecessor.
Answer True (T).
Explanation
The counting numbers are called Natural numbers.
Thus, 1, 2, 3, 4, 5, 6, . . . . are natural numbers.
Thus, 1 is the smallest natural numbers.
And, the number comes just before a number is called the predecessor of the given number.
Here, since 1 is the smallest natural number, thus there is no natural number before 1.
Thus, the given statement "The natural number 1 has no predecessor" is true (T).
(j) The whole number 1 has no predecessor.
Answer False (F).
The correct statement is "Zero (0) is the predecessor of natural number 1"
Explanation
The natural numbers along with zero (0) are called the whole numbers.
Thus, 0, 1, 2, 3, 4, 5, . . . . are whole numbers.
The number comes just before a given number is called the predecessor of the number.
This, means we can get the predecessor of a number by subtracting 1 from the given number.
Thus, predecessor of whole number 1
= 1 – 1 = 0
Thus, 0 (zero) is the predecessor of the whole number 1.
Thus, the given statement "The whole number 1 has no predecessor" is false (F).
(k) The whole number 13 lies between 11 and 12.
Answer False (F)
Explanation
Since, 13 is greater than 11 and 12, thus, 13 lies right to 12 on a number line.
And, since 11 and 12 both are whole numbers and 11 is the predecessor of 12, thus, there is no whole number lie between 11 and 12.
Thus, the given statement "The whole number 13 lies between 11 and 12" is false (F).
The correct statement is "The whole number 13 lies left to 12 on a number line".
(l) The whole number 0 has no predecessor.
Answer True (T).
Explanation
The natural numbers along with zero (0) are called the Whole Numbers.
This means, 0, 1, 2, 3, 4, . . . . . are whole numbers.
Here, zero (0) is the smallest whole number.
The number comes just before a given number is called the predecessor of the number. This means we can get the predecessor of a given number by subtracting 1 from the given number.
Here, since zero (0) is the smallest whole numbers, hence there is no whole number smaller than zero (0).
Thus, the given statement "The whole number 0 has no predecessor" is True (T).
(m) The successor of a two-digit number is always a two-digit number.
Answer False (F).
Explanation
The number come just after a number is called the successor of the given number.
This means we can get the successor a given number by adding 1 to the given number.
Thus, the successor of 50
= 50 + 1 = 51
And, the successor of 99
= 99 + 1 = 100
Here, 99 is a two-digit number, and 100 is a three-digit number.
And, 100 is the successor of the two-digit number 99.
Thus, the given statement "The successor a two-digit number is always a two-digit number" is false (F).
The correct statement is "The successor of a two-digit number can be a two-digit number or three-digit number both."