Which of the following mathematical statements is true?

The correct statement is: Zero is called an additive identity for whole numbers.

Let us analyze each mathematical statement step-by-step to understand why this is the case:

1. Statement: "Mathematics is based only on observations and experiments."
This statement is incorrect. While empirical sciences like physics and chemistry rely heavily on observation and experimentation, mathematics is a deductive science. It is built on logical reasoning, axioms, definitions, and rigorous proofs.

2. Statement: "Zero is called the multiplicative identity for whole numbers."
This statement is incorrect. The multiplicative identity is a number that, when multiplied by any whole number, leaves the number unchanged. For any whole number $a$:

$a\times 1=a$

Therefore, 1 is the multiplicative identity. Multiplying any whole number by 0 results in 0, not the number itself.

3. Statement: "Commutative law holds true for the operation of ‘division’."
This statement is incorrect. The commutative law states that changing the order of the operands does not change the result. For division to be commutative, we would need $a÷b=b÷a$ for all whole numbers $a$ and $b$. However, if we take $a=4$ and $b=2$:

$4÷2=2$

But when we reverse the order:

$2÷4=0.5$

Since $2\ne 0.5$, division is not commutative.

4. Statement: "Zero is called an additive identity for whole numbers."
This statement is correct. An additive identity is a number that, when added to any whole number, gives the original number. For any whole number $a$:

$a+0=a$

For example, if $a=5$, then $5+0=5$. Since the identity of the number is preserved under addition, zero is indeed the additive identity for whole numbers.