Question

Which of the following statements are true and which are false?

(i) Every whole number has its successor.
(ii) Every whole number has its predecessor.
(iii) 0 is the smallest natural number.
(iv) 1 is the smallest whole number.
(v) 0 is less than every natural number.
(vi) Between any two whole numbers there is a whole number.
(vii) Between any two non-consecutive whole numbers there is a whole number.
(viii) The smallest 5-digit number is the successor of the largest 4 digit number
(ix) Of the given two natural numbers, the one having more digits is greater.
(x) The predecessor of a two digit number cannot be a single digit number.
(xi) If a and b are natural numbers and a < b, than there is a natural number c such that a<b<c.
(xii) If a and b are whole numbers and a<b, then a+1< b+1.
(xiii) The whole number 1 has 0 as predecessor.
(xiv) The natural number 1 has no predecessor.

Answer 1

(i) True
The successor of every whole number can be found by adding 1.
(ii) False
Zero (0) is a whole number whose predecessor (-1) is not a whole number.
(iii) False
1 is the smallest natural number.
(iv) False
Zero (0) is the smallest whole number.
(v) True
The smallest natural number is 1, so zero (0) is less than every natural number.
(vi) False
There is no whole number between two consecutive whole numbers.
(vii) True
(viii) True
The smallest five-digit number = 10,000
The largest four-digit number = 9,999
Difference = 10,000 - 9,999 = 1
Because the difference is 1, 10,000 is the successor of 9,999.
(ix) True
(x) False
10 is a two-digit number whose predecessor is 9, which is a one-digit number.
(xi) False
If a and b are consecutive natural numbers, then there cannot be any natural number c in between a and b.
(xii) True
(xiii) True
(xiv) True
The predecessor of natural number 1 is 0, which is not a natural number.