A = set of all trianglesB = set of all right trianglesA – B=?a)s...
A = Set of all triangles
B = Set of all right triangles
A – B = Set of triangles after removing all right triangles from A
= Set of all triangles which do not have right angle
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A = set of all trianglesB = set of all right trianglesA – B=?a)s...
D because set aA contains all the triangles. and set B contains only right angled triangles Thus A-B is all triangles excluding right angled triangles
A = set of all trianglesB = set of all right trianglesA – B=?a)s...
Understanding the Sets
To comprehend the relationship between sets A and B:
- Set A: This is the set of all triangles. This includes all varieties of triangles, such as scalene, isosceles, equilateral, and right triangles.
- Set B: This is the set of all right triangles, which specifically includes triangles that have one angle equal to 90 degrees.
Analyzing A ∩ B
When we look at the intersection of sets A and B (A ∩ B), we are identifying the elements that belong to both sets:
- Elements in A ∩ B: These are triangles that are both considered triangles and also have a right angle.
Evaluating the Options
Now, let’s analyze the provided options:
- Option A: Set of all equilateral triangles - This does not belong in A ∩ B because equilateral triangles have no right angles.
- Option B: Set of all triangles which have all three angles different - This includes scalene triangles and does not necessarily intersect with right triangles.
- Option C: Set of all isosceles triangles - While some isosceles triangles can be right triangles, not all of them are, so this option is not correct for A ∩ B.
- Option D: Set of all triangles which do not have one right angle - This correctly describes the elements in A that are not in B, making it the complement of set B within set A.
Conclusion
Thus, the correct answer is option D: the set of all triangles which do not have one right angle, as it accurately represents the triangles in A that do not belong to B.