Which of the following statements are true and which are false?
(a) Zero is the smallest natural number.
(b) 400 is the predecessor of 399.
(c) 600 is the successor of 599.
(d) All-natural numbers are whole numbers.
(e) All whole numbers are natural numbers.
(f) The predecessor of a two-digit number is never a single-digit number.
(g) 1 is the smallest whole number.
(h) The natural number 1 has no predecessor.
(i) The whole number 1 has no predecessor.
(j) The whole number 13 lies between 11 and 12.
(k) The whole number 0 has no predecessor.
(l) The successor of a two-digit number is always a two-digit number.

Solution:

Let us find out which statements are true and which are false.

(a) Zero is the smallest natural number. (F) 
We know that zero is not a natural number, hence, it can't be the smallest natural number.

(b) 400 is the predecessor of 399. (F) 
The predecessor of any number is the one that comes before the given number on the number line. 
We know that 400 comes after 399 on the number line. Hence, it is not the predecessor.

(c) 600 is the successor of 599. (T) 
The successor of any number is the one that comes after the given number on the number line. 
We know that 600 comes after 599 on the number line. Hence, it is the successor.

(d) All natural numbers are whole numbers. (T) 
Natural numbers are included in the set of whole numbers. Hence, all natural numbers are whole numbers. 

(e) All whole numbers are natural numbers. (F) 
All whole numbers except 0 are natural numbers. Hence, all whole numbers are not natural numbers.

(f) The predecessor of a two-digit number is never a single-digit number. (F) 
A predecessor comes before the given number on a number line. Hence, it is possible that a single-digit number can come before a two-digit number. For example, 9 is the predecessor of 10.

(g) 1 is the smallest whole number. (F) 
Whole numbers start their count from zero, hence, zero is the smallest whole number. 

(h) The natural number 1 has no predecessor. (T) 
Since natural numbers start from 1, it has no predecessor in this list.

(i) The whole number 1 has no predecessor. (F)
The set of whole numbers starts from 0, 1, 2, 3..., therefore, 1 has a predecessor - zero.

(j) The whole number 13 lies between 11 and 12. (F) 
13 is a successor of 12. Hence, it does not lie between 11 or 12. 

(k) The whole number 0 has no predecessor. (T)
The set of whole numbers starts from 0, 1, 2, 3...This shows that in this set, 0 has no predecessor.

(l) The successor of a two-digit number is always a two-digit number. (F)
A successor comes after the given number on a number line. In the case of 99 (a two-digit number), the successor is 100 which is a three-digit number.

Thus,
(a) Zero is the smallest natural number. (F) 
(b) 400 is the predecessor of 399. (F) 
(c) 600 is the successor of 599. (T) 
(d) All natural numbers are whole numbers. (T) 
(e) All whole numbers are natural numbers. (F) 
(f) The predecessor of a two-digit number is never a single-digit number. (F) 
(g) 1 is the smallest whole number. (F) 
(h) The natural number 1 has no predecessor. (T) 
(i) The whole number 1 has no predecessor. (F) 
(j) The whole number 13 lies between 11 and 12. (F) 
(k) The whole number 0 has no predecessor. (T)
(l) The successor of a two-digit number is always a two-digit number. (F)

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

Summary:

(a) Zero is the smallest natural number - (F), (b) 400 is the predecessor of 399 - (F), (c) 600 is the successor of 599 - (T), (d) All natural numbers are whole numbers - (T), (e) All whole numbers are natural numbers - (F), (f) The predecessor of a two-digit number is never a single-digit number - (F), (g) 1 is the smallest whole number - (F), (h) The natural number 1 has no predecessor - (T), (i) The whole number 1 has no predecessor - (F), (j) The whole number 13 lies between 11 and 12 - (F), (k) The whole number 0 has no predecessor - (T), (l) The successor of a two-digit number is always a two-digit number - (F)