Solution:
We will be using the concepts of natural numbers, whole numbers, and consecutive numbers to determine whether the statements given below are True or False.
You are viewing: Which Of The Following Statements Is False N Natural Numbers
(a) Zero is the smallest natural number- False [N = {1, 2, 3, ……….}, 0 is not a natural number]
(b) 400 is the predecessor of 399 – False [The predecessor of 399 is 398. (399 – 1 = 398)]
(c) Zero is the smallest whole number – True [W = {0, 1, 2, 3, ……….}, the whole numbers begin with 0.]
(d) 600 is the successor of 599 – True [599 + 1 = 600]
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(e) All natural numbers are whole numbers – True N = {1, 2, 3, ……….} W = {0, 1, 2, 3, ……….} As we see that every element of natural numbers set (N) belongs to the set of whole numbers (W) thus, N belongs to W.
(f) All whole numbers are natural numbers – False N = {1, 2, 3, ……….} W = {0, 1, 2, 3, ……….} 0 is a whole number but is not a natural number.
(g) The predecessor of a two-digit number is never a single-digit number- False [The predecessor of 10 is 9 which is a single-digit number]
(h) 1 is the smallest whole number- False [0 is the smallest whole number.]
(i) The natural number 1 has no predecessor -True [The predecessor of 1 is 0 but is not a natural number]
(j) The whole number 1 has no predecessor – False [0 is the predecessor of 1 and is a whole number]
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(k) The whole number 13 lies between 11 and 12.- False [13 lies between 12 and 14. No whole number lies between 11 and 12 as they are consecutive numbers]
(l) The whole number 0 has no predecessor. – True [The predecessor of 0 is -1 and is not a whole number. -1 is an integer.]
(m) The successor of a two-digit number is always a two-digit number – False [The successor of 99 is 100 which is a 3-digit number]
NCERT Solutions for Class 6 Maths Chapter 2 Exercise 2.1 Question 8
Which of the following statements are true (T) and which are false (F)? (a) Zero is the smallest natural number. (b) 400 is the predecessor of 399. (c) Zero is the smallest whole number. (d) 600 is the successor of 599. (e) All natural numbers are whole numbers. (f) All whole numbers are natural numbers. (g) The predecessor of a two-digit number is never a single-digit number. (h) 1 is the smallest whole number (i) The natural number 1 has no predecessor. (j) The whole number 1 has no predecessor. (k) The whole number 13 lies between 11 and 12. (l) The whole number 0 has no predecessor. (m) The successor of a two-digit number is always a two-digit number.
Summary:
(a) Zero is the smallest natural number is a false statement since 0 is not a natural number. (b) 400 is the predecessor of 399 is a false statement since the predecessor of 399 is 398. (c) Zero is the smallest whole number is a true statement since the set of whole numbers begin with 0. (d) 600 is the successor of 599 is a true statement. (e) All-natural numbers are whole numbers is a true statement since natural numbers are a subset of whole numbers. (f) All whole numbers are natural numbers is a false statement since 0 is a whole number but is not a natural number. (g) The predecessor of a two-digit number is never a single-digit number is a false statement since the predecessor of 10 is 9. (h) 1 is the smallest whole number is a false statement since 0 < 1 and 0 is a whole number. (i) The natural number 1 has no predecessor is a true statement since the predecessor 0 is not a natural number. (j) The whole number 1 has no predecessor is a false statement since 0 is the predecessor of 1 and is the whole number. (k) The whole number 13 lies between 11 and 12 is a false statement since 13 > 12 > 11. (l) The whole number 0 has no predecessor is a true statement since the predecessor -1 is not a whole number. (m) The successor of a two-digit number is always a two-digit number is a false statement since the successor of 99, a two-digit number is 100, a three-digit number.
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Category: WHICH
