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Definition of Relations

Statement 1: ...

Question

Statement 1: $| z_{1} - a | < a, | z_{2} - b | < b, | z_{3} - c | < c$ , where a, b, c are positive real numbers, then $| z_{1} + z_{2} + z_{3} |$ is greater than $2 | a + b + c |$ .
Statement 2: $| z_{1} \pm z_{2} | \leq | z_{1} | + | z_{2} |$ .

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

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Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.

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Statement 1 is true and Statement 2 is false.

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Statement 1 is false and Statement 2 is true.

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Solution

The correct option is D Statement 1 is false and Statement 2 is true.
$| z_{1} + z_{2} + z_{3} | = | z_{1} - a + z_{2} - b + z_{3} - c + (a + b + c) |$
$\leq | z_{1} - a | + | z_{2} - b | + | z_{3} - c | + | a + b + c |$
$\leq 2 | a + b + c |$
Hence, $| z_{1} + z_{2} + z_{3} |$ is less than $2 | a + b + c |$ .
Statement 1 is false and Statement 2 is true

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Similar questions

| z_{1} - a | < a, | z_{2} - b | < b, | z_{3} - c | < c

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