CA Foundation Exam > CA Foundation Questions > Given A = {2, 3}, B = {4, 5}, C = {5, 6} then...
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Given A = {2, 3}, B = {4, 5}, C = {5, 6} then A × (B ∩ C) is
- a){(2, 5), (3, 5)}
- b){(5, 2), (5, 3)}
- c){(2, 3), (5, 5)}
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Given A = {2, 3}, B = {4, 5}, C = {5, 6} then A (B C) isa){(2, 5), (...
Given sets A, B, and C as A = {2, 3}, B = {4, 5}, C = {5, 6}, we need to find the result of the expression A (B C).
To find the result, we need to perform the set operations in the given expression step by step.
1. B C:
- The symbol represents the set intersection operation, which means we need to find the common elements between sets B and C.
- B = {4, 5} and C = {5, 6}.
- The common element between B and C is 5.
- Therefore, B C = {5}.
2. A (B C):
- The symbol represents the set union operation, which means we need to find the elements that are present in either set A or the result of the previous operation (B C).
- A = {2, 3} and (B C) = {5}.
- The elements present in either A or (B C) are 2, 3, and 5.
- Therefore, A (B C) = {2, 3, 5}.
Therefore, the correct answer is option 'A': {(2, 5), (3, 5)}.
To find the result, we need to perform the set operations in the given expression step by step.
1. B C:
- The symbol represents the set intersection operation, which means we need to find the common elements between sets B and C.
- B = {4, 5} and C = {5, 6}.
- The common element between B and C is 5.
- Therefore, B C = {5}.
2. A (B C):
- The symbol represents the set union operation, which means we need to find the elements that are present in either set A or the result of the previous operation (B C).
- A = {2, 3} and (B C) = {5}.
- The elements present in either A or (B C) are 2, 3, and 5.
- Therefore, A (B C) = {2, 3, 5}.
Therefore, the correct answer is option 'A': {(2, 5), (3, 5)}.
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Community Answer
Given A = {2, 3}, B = {4, 5}, C = {5, 6} then A (B C) isa){(2, 5), (...
To solve the given problem, we need to understand the concept of set operations and the properties of sets.
The operation given in the question is the intersection of sets. The intersection of two sets A and B, denoted by A ∩ B, is the set of elements that are common to both A and B. In other words, it includes all the elements that are present in both A and B.
In this case, we need to find the intersection of sets A, B, and C. Let's solve it step by step.
Step 1: Find the intersection of set B and set C.
- Set B = {4, 5}
- Set C = {5, 6}
The common element between B and C is 5. Therefore, the intersection of B and C is {5}.
Step 2: Find the intersection of set A and the intersection of B and C.
- Set A = {2, 3}
- The intersection of B and C = {5}
The common element between A and the intersection of B and C is 5. Therefore, the intersection of A and the intersection of B and C is {5}.
Step 3: Finalize the answer.
The intersection of A and the intersection of B and C is {5}. However, we need to represent it as ordered pairs. Since the only common element is 5, we can represent it as (2, 5) and (3, 5). Therefore, the final answer is {(2, 5), (3, 5)}.
Therefore, the correct answer is option A) {(2, 5), (3, 5)}.
The operation given in the question is the intersection of sets. The intersection of two sets A and B, denoted by A ∩ B, is the set of elements that are common to both A and B. In other words, it includes all the elements that are present in both A and B.
In this case, we need to find the intersection of sets A, B, and C. Let's solve it step by step.
Step 1: Find the intersection of set B and set C.
- Set B = {4, 5}
- Set C = {5, 6}
The common element between B and C is 5. Therefore, the intersection of B and C is {5}.
Step 2: Find the intersection of set A and the intersection of B and C.
- Set A = {2, 3}
- The intersection of B and C = {5}
The common element between A and the intersection of B and C is 5. Therefore, the intersection of A and the intersection of B and C is {5}.
Step 3: Finalize the answer.
The intersection of A and the intersection of B and C is {5}. However, we need to represent it as ordered pairs. Since the only common element is 5, we can represent it as (2, 5) and (3, 5). Therefore, the final answer is {(2, 5), (3, 5)}.
Therefore, the correct answer is option A) {(2, 5), (3, 5)}.
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Given A = {2, 3}, B = {4, 5}, C = {5, 6} then A (B C) isa){(2, 5), (3, 5)}b){(5, 2), (5, 3)}c){(2, 3), (5, 5)}d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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