If a denotes the absolute value of an integer then which of the following are correct 1 ab a b 2 a b...........

Mathematics (NDA) Complex Numbers

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If |a| denotes the absolute value of an integer, then which of the following are correct?

1.|ab|=|a||b|

2. |a+b|≤|a|+|b|

3. |a−b|≥||a|−|b||

Select the correct answer using the code given below.

1 and 2 only

2 and 3 only

1 and 3 only

1, 2 and 3

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Explanation:

Given |a| is the absolute value of an integer,
From the definition,
|a|=a if a≥0,
=−a is a≤0
∴ |ab|=|a||b| where a,b are real numbers.
We know that from the triangle inequality sum of any two sides is always greater than the third side,
i.e.,|a+b|≤|a|+|b|,
We can also prove by considering
Absolute part of the difference between any two sides is always less than the third side,
= |a−b|≥||a|−|b||