# 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.

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To do :

We have to find whether the given statements are true or false.

Solution:

(a) Natural numbers are 1, 2, 3, ...... and so on.

Therefore,

0 is not a natural number.

The given statement is false.

(b) The predecessor of a number is the number that comes just before it.

The predecessor of a number $x$ is $x−1$.

Therefore,

The predecessor of 400 is $400-1=399$.

The given statement is false.

(c) Whole numbers are 0, 1, 2, 3, ...... and so on.

Therefore,

0 is the smallest whole number.

The given statement is true.

(d) The successor of a number is the number that comes just after it.

The successor of a number x is $x+1$.

Therefore,

The successor of 599 is $599+1=600$.

The given statement is true.

(e) Natural numbers are 1, 2, 3, ...... and so on.

Whole numbers are 0, 1, 2, 3, ...... and so on.

Therefore,

All natural numbers are whole numbers.

The given statement is true.

(f) Natural numbers are 1, 2, 3, ...... and so on.

Whole numbers are 0, 1, 2, 3, ...... and so on.

Therefore,

0 is a whole number but not a natural number.

The given statement is false.

(g) The predecessor of a number is the number that comes just before it.

The predecessor of a number $x$ is $x−1$.

Therefore,

The predecessor of 10 is $10-1=9$.

The given statement is false.

(h) Natural numbers are 1, 2, 3, ...... and so on.

Whole numbers are 0, 1, 2, 3, ...... and so on.

Therefore,

1 is the smallest natural number and 0 is the smallest whole number.

The given statement is false.

(i) Natural numbers are 1, 2, 3, ...... and so on.

Therefore,

There is no natural number smaller than 0.

This implies,

The predecessor of 1 is 0 but is not a natural number.

The given statement is true.

(j) Whole numbers are 0, 1, 2, 3, ...... and so on.

The predecessor of a number is the number that comes just before it.

The predecessor of a number $x$ is $x−1$.

Therefore,

The predecessor of 1 is $1-1=0$.

The given statement is false.

(k) There is no whole number between 11 and 12.

The number 13 comes after 12.

The given statement is false.

(l) Whole numbers are 0, 1, 2, 3, ...... and so on.

The predecessor of a number is the number that comes just before it.

There is no whole number smaller than 0.

The given statement is true.

(m) The successor of a number is the number that comes just after it.

The successor of a number x is $x+1$.

Therefore,

The successor of 99 is $99+1=100$.

The given statement is false.

Updated on 10-Oct-2022 13:29:41