Maths-
General
Easy
Question
For any two sets A and B, if
and
for some set X , then
![A minus B equals A intersection B](data:image/png;base64,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)
![A equals B](data:image/png;base64,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)
![B minus A equals A intersection B](data:image/png;base64,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)
- None of these
The correct answer is: ![A equals B](data:image/png;base64,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)
Given, ![A intersection X equals B intersection X equals ϕ](data:image/png;base64,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)
A and X,B and X are disjoint sets.
![text Also, end text A union X equals B union X not stretchy rightwards double arrow A equals B](data:image/png;base64,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)
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for constructive interference at P between the ray
and reflected ray ![O P](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAANCAYAAABCZ/VdAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAARVJREFUeNpjYMAO9IB4LhC/BOJPQLwQiLVwqP0BxP+h+AsQrwJiRxxqGWqBeAMQmwIxExQHAPFDIDZHU6sCxBeQ+GxA7ALE97E5phqIZ+Kw1BHNIAaopUuxqE0G4hJkATUgvgF1KS4ACiJBJH49uiFQ0AHEOcgCPegCWMBuILZF4oPC1w9NjSgQ3wJiYWTBK0AsT8Dwx0DMh8QHGSKJxDcG4qPoEQoKim8EDGYB4g9oev5AU8k7qKHNaJbBY/kTAcNDgXgxEh+UcvYzEAFArvhFIDKPoiXFSCCez0Ak2ALEiTjkKrEk0UlAnEas4SrQpBgPDV8QMIAGBba0vw6IvRhIALLQbA+KoNfQDGKJQy1IDQfDQAEA8+k0isiZVGcAAABTdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPk88L21pPjxtaT5QPC9taT48L21hdGg+VjfoXwAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
In the adjacent diagram,
represents a wavefront and
and
, the corresponding two rays. Find the condition on
for constructive interference at P between the ray
and reflected ray ![O P](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General