State whether the following statements are true (T) or false (F):

(i) The successor of a one-digit number is always a one-digit number.

(ii) The predecessor of every two-digit number is a one-digit number.

(iii) The predecessor of a 3-digit number is always a 3-digit number.

(iv) The successor of a 3-digit number is always a 3-digit number.

(v) If a is any whole number, then a ÷ a = 1

(vi) If a is any non-zero whole number, then 0 ÷ a = 0

(vii) On adding two different whole numbers, we always get a natural number.

(viii) Between two whole numbers there is a whole number.

(ix) There is a natural number which when added to a natural number, gives that number.

(x) If the product of two whole numbers is zero, then at least one of them is zero.

(xi) Any non-zero whole number divided by itself gives the quotient 1.

(i) False.

Reason: The successor of 9 (a one-digit number) is 10, which is a two-digit number.

(ii) False.

Reason: The predecessor of 99 (a two-digit number) is 98, which is also a two-digit number.

(iii) False.

Reason: The predecessor of 100 (a 3-digit number) is 99, which is a 2-digit number.

(iv) False.

Reason: The successor of 999 (a 3-digit number) is 1000, which is a 4-digit number.

(v) False.

Reason: If a = 0, then a ÷ a = 0 ÷ 0 is not defined. So, the statement is not true for all whole numbers.

(vi) True.

Reason: Zero divided by any non-zero whole number is always 0. For example, 0 ÷ 5 = 0.

(vii) True.

Reason: When two different whole numbers are added, at least one of them is non-zero. So, the sum is at least 1, which is a natural number.

(viii) False.

Reason: Between two consecutive whole numbers (such as 5 and 6), there is no whole number.

(ix) False.

Reason: The number 0, when added to any natural number, gives that number. But 0 is not a natural number. There is no natural number that acts as the additive identity for natural numbers.

(x) True.

Reason: If a × b = 0, then either a = 0 or b = 0 (or both).

(xi) True.

Reason: Any non-zero whole number a satisfies a ÷ a = 1, since a × 1 = a.