If A and B are sets and A ∪ B = A ∩ B then which of the following is(are) true?
Either one of A or B is empty set
B is proper subset of A
A = B
A is proper subset of B
Answers
Answer:
Union & Intersection are equal means A = B
SOLUTION
TO CHOOSE THE CORRECT OPTION
If A and B are sets and A ∪ B = A ∩ B then which of the following is(are) true
- Either one of A or B is empty set
- B is proper subset of A
- A = B
- A is proper subset of B
EVALUATION
Here it is given that A and B are sets and A ∪ B = A ∩ B
Now we show that A ∪ B = A ∩ B implies A = B
Let x ∈ A
⇒ x ∈ A ∪ B
⇒ x ∈ A ∩ B
⇒ x ∈ B
∴ A ⊆ B - - - - - (1)
Next let x ∈ B
⇒ x ∈ A ∪ B
⇒ x ∈ A ∩ B
⇒ x ∈ A
∴ B ⊆ A - - - - - (2)
From Equation 1 and Equation 2 we get
A = B
FINAL ANSWER
Hence the correct option is A = B
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