Q14. ‘(1 2) 3 = 1 (2 3)’ The above is known as (a) commutativi...
**Answer:**
The above equation, ‘(1 2) 3 = 1 (2 3)’ shows the application of a mathematical property known as **associativity**.
**Associativity** is a property of binary operations (operations that involve two elements) and it determines the way in which parentheses can be placed when performing the operation. It states that the way in which the elements are grouped does not affect the result of the operation.
In the given equation, we have two sets of parentheses enclosing the numbers. Let's break down the equation to understand it better:
- (1 2) 3: This expression involves two operations, the operation inside the first set of parentheses and then the operation between the result and the number 3.
- The operation inside the first set of parentheses is addition (represented by the symbol '+'). So, (1 2) equals 3.
- The next operation is the addition between 3 and the number 3. So, 3 + 3 equals 6.
- 1 (2 3): This expression also involves two operations, the operation inside the second set of parentheses and then the operation between the number 1 and the result.
- The operation inside the second set of parentheses is addition. So, (2 3) equals 5.
- The next operation is the addition between the number 1 and 5. So, 1 + 5 equals 6.
As we can see, both expressions yield the same result, which is 6. This demonstrates the **associativity** of addition. The way in which the numbers are grouped (whether (1 2) 3 or 1 (2 3)) does not change the final result of the addition operation.
Hence, the correct answer is **(b) associativity of addition**.
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