# 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.

(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.

## Answer: In the following statements T is for true and F is for false.

(a) Zero is the smallest natural number. (F)

(b) 400 is the predecessor of 399. (F)

(d) 600 is the successor of 599. (T)

(e) All-natural numbers are whole numbers. (T)

(f) All whole numbers are natural numbers. (F)

(g) The predecessor of a two-digit number is never a single-digit number. (F)

(h) 1 is the smallest whole number. (F)

(i) The natural number 1 has no predecessor. (F)

(j) The whole number 1 has no predecessor. (F)

(k) The whole number 13 lies between 11 and 12. (F)

(l) The whole number 0 has no predecessor. (F)

(m) The successor of a two-digit number is always a two-digit number. (F)

## Explanation:

Let's find 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.

(d) 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.

(e) All-natural numbers are whole numbers. (T)

Natural numbers are the ones that have positive integers. Hence, all positive integers are whole numbers.

(f) All whole numbers are natural numbers. (F)

Natural numbers are the ones who have positive integers. Hence, all positive integers are whole numbers, but converse is not true.

(g) The predecessor of a two-digit number is never a single-digit number. (F)

Predecessor comes before the given number on a numberline. Hence, it is possible that a single-digit number can come bofore a two-digit number.

(h) 1 is the smallest whole number. (F)

Whole numbers start their count from zero, hence making zero the smallest whole number.

(i) The natural number 1 has no predecessor. (F)

Although 1 is a natural number, it has a predecessor - zero.

(j) The whole number 1 has no predecessor. (F)

Although 1 is a natural number, it has a predecessor - zero.

(k) The whole number 13 lies between 11 and 12. (F)

13 is a successor of 12. Hence it does not lie between any of 11 or 12.

(l) The whole number 0 has no predecessor. (F)

Although 0 is a whole number, it has a predecessor - negative 1.

(m) The successor of a two-digit number is always a two-digit number. (F)

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.

**Thus,**

**(a) Zero is the smallest natural number. (F) **

(b) 400 is the predecessor of 399. (F)

(d) 600 is the successor of 599. (T)

(e) All-natural numbers are whole numbers. (T)

(f) All whole numbers are natural numbers. (F)

(g) The predecessor of a two-digit number is never a single-digit number. (F)

(h) 1 is the smallest whole number. (F)

(i) The natural number 1 has no predecessor. (F)

(j) The whole number 1 has no predecessor. (F)

(k) The whole number 13 lies between 11 and 12. (F)

(l) The whole number 0 has no predecessor. (F)

(m) The successor of a two-digit number is always a two-digit number. (F)

(b) 400 is the predecessor of 399. (F)

(d) 600 is the successor of 599. (T)

(e) All-natural numbers are whole numbers. (T)

(f) All whole numbers are natural numbers. (F)

(g) The predecessor of a two-digit number is never a single-digit number. (F)

(h) 1 is the smallest whole number. (F)

(i) The natural number 1 has no predecessor. (F)

(j) The whole number 1 has no predecessor. (F)

(k) The whole number 13 lies between 11 and 12. (F)

(l) The whole number 0 has no predecessor. (F)

(m) The successor of a two-digit number is always a two-digit number. (F)