Question

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.

Answer 1

Determine the statements that are true and false.

a) Zero is the smallest natural number.

It is “False” because $0$ is not a natural number. It is a whole number.

b) $400$is the predecessor of $399$.

It is “False” because the predecessor of $399$is $(399–1)=398$.

c) Zero is the smallest whole number.

It is “True” because the whole numbers begin with $0$.

d) $600$is the successor of $599$.

It is “True” because $599+1=600$ so $600$is the successor of $599$.

e) All-natural numbers are whole numbers.

It is “True” because when we add $0$ to the list of all-natural numbers we get all whole numbers.

So natural numbers are a sub set of Whole numbers.

f) All whole numbers are natural numbers.

It is “False” because $0$ is a whole number but not a natural number.

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

It is “False” because the predecessor of $10$ is $10-1=9$ which is a single-digit number

h) $1$is the smallest whole number.

It is “False” because the $0$ is the smallest whole number.

i) The natural number $1$has no predecessor.

It is “True” because the predecessor of $1$ is $0$, which is not a natural number but is whole number.

So we can say that the natural number $1$has no predecessor in natural numbers, but it has a predecessor in whole numbers.

j) The whole number $1$has no predecessor.

It is “False” because $0$ is the predecessor of $1$ and is a whole number.

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

It is “False” because $13$ lies between $12$ and $14$. Also no whole number lies between $11$ and $12$ as they are consecutive numbers

l) The whole number $0$ has no predecessor.

It is “True” because the predecessor of $0$ is $-1$ and is not a whole number, $-1$ is an integer.

So we can say that whole number $0$ has no predecessor in whole numbers but has a predecessor in integers.

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

It is “False” because the successor of $99$is $100$ which is a three-digit number.