Let A, B and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. show that B = C.
Answers
Answered by
8
According to the question,
A ∪ B = A ∪ C
And,
A ∩ B = A ∩ C
To show,
B = C
Let us assume,
x ∈ B
So,
x ∈ A ∪ B
x ∈ A ∪ C
Hence,
x ∈ A or x ∈ C
When x ∈ A, then,
x ∈ B
∴ x ∈ A ∩ B
As, A ∩ B = A ∩ C
So, x ∈ A ∩ C
∴ x ∈ A or x ∈ C
x ∈ C
∴ B ⊂ C
Similarly,
it can be shown that C ⊂ B
Hence, B = C
Answered by
46
Answer:
➡According to the question,
A ∪ B = A ∪ C
And,
A ∩ B = A ∩ C
➡To show,
B = C
➡Let us assume,
x ∈ B
So,
x ∈ A ∪ B
x ∈ A ∪ C
➡Hence,
x ∈ A or x ∈ C
When x ∈ A, then,
x ∈ B
∴ x ∈ A ∩ B
As, A ∩ B = A ∩ C
So, x ∈ A ∩ C
∴ x ∈ A or x ∈ C
x ∈ C
∴ B ⊂ C
Similarly,
it can be shown that C ⊂ B
➡Hence, B = C
Step-by-step explanation:
HOPE IT HELP YOU ✌✌
Similar questions