Which of the following is false:
(i) $| 4 + 2 | = | 4 | + | 2 |$
(ii) $| 2 - 4 | = | 2 | + | 4 |$
(iii) $| 4 - 2 | = | 4 | - | 2 |$
(iv) $| (- 2) + (- 4) | = | - 2 | + | - 4 |$

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Solution

Since, we have $| - a | = | a | = a$
(i) To verify $| 4 | + | 2 | = | 4 | + | 2 |$ :
L.H.S $= | 4 + 2 |$
$= | 6 |$
Therefore, L.H.S $= 6$ .......(i)
R.H.S $= | 4 | + | 2 |$
$= 4 + 2$
Therefore, R.H.S $= 6$ ......(ii)
From equation (i) and (ii), we get $| 4 + 2 | = | 4 | + | 2 |$
Hence, the given expression is true .
(ii) To verify $| 2 - 4 | = | 2 | + | 4 |$ :
L.H.S $= | 2 - 4 |$
$= | - 2 |$
$= 2$
Therefore, L.H.S $= 2$ ......(iii)
R.H.S $= | 2 | + | 4 |$
$= 2 + 4$
$= 6$
Therefore, R.H.S $= 6$ ......(iv)
From equation(iii) and (iv), we get
L.H.S $\neq$ R.H.S
Hence, the given expression is false.
(iii) To verify $| 4 - 2 | = | 4 | - | 2 |$ ;
L.H.S $= | 4 - 2 |$
$= | 2 |$
Therefore, L.H.S $= 2$ .......(i)
R.H.S $= | 4 | - | 2 |$
$= 4 - 2$
Therefore, R.H.S $= 2$ .....(ii)
From equation(i) and (ii), we have L.H.S $=$ R.H.S.
Hence, the given expression is true.
(iv) To verify $| (- 2) + (- 4) | = | - 2 | + | (- 4) |$ ;
L.H.S $= | (- 2) + (- 4) |$
$= | - 2 - 4 |$
$= | - 6 |$
$= 6$
Therefore, L.H.S $= 6$ ........(i)
R.H.S $= | - 2 | + | (- 4) |$
$= 2 + 4$
$= 6$
Therefore, R.H.S $= 6$ .......(ii)
From equation (i) and (ii), we get
L.H.S $=$ R.H.S
Hence, the given expression is true.

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Which of the following is false:(i) |4+2|=|4|+|2| (ii) |2−4|=|2|+|4|(iii) |4−2|=|4|−|2|(iv) |(−2)+(−4)|=|−2|+|−4|

Which of the following is false:
(i) $| 4 + 2 | = | 4 | + | 2 |$
(ii) $| 2 - 4 | = | 2 | + | 4 |$
(iii) $| 4 - 2 | = | 4 | - | 2 |$
(iv) $| (- 2) + (- 4) | = | - 2 | + | - 4 |$