If A= [-3, 5), B = (0, 6] then find (i) A- B, (ii) A n B
Answers
Answer:
step by step explanation
A={-3, -2, -1, 0,1,2,3,4] and B={1, 2,3,4,5,6]
(i)A-B
={-3, -2, -1,0, 5,6]
(ii) A U B
A U B ={-3, -2, -1, 0,1,2,3,4,5,6]
A U B ={-3, 6]
Answer:
(i) A - B = [-3, 0]
(ii) A∩B =(0,5)
Step-by-step explanation:
Given
A= [-3, 5), B = (0, 6]
To find,
(i) A- B,
(ii) A∩B
Recall the concepts
A- B is the set of elements that belongs to the set A but does not belong to set B
A∩B is the set of elements that are common to sets A and B.
Solution
(i) we have A= [-3, 5)
we can split this interval into two intervals such that
[-3, 5) = [-3, 0] ∪ (0, 5)
These two intervals [-3, 0] ,(0, 5) are disjoint intervals such that
None of the elements in the interval [-3, 0] belongs to (0, 5)
therefore, None of the elements in the interval [-3, 0] belongs to (0, 6]
Hence none of the elements in the interval [-3, 0] belongs to B
∴A - B = [-3, 0]
(ii) we have A= [-3, 5), B = (0, 6]
we can express the interval A as disjoint intervals as
A = [-3, 5) = [-3, 0] ∪(0, 5)
B = (0, 6] = (0,5) ∪[5,6]
Here,
In these two sets of intervals, the interval which is common to both A and B are (0,5)
∴A∩B =(0,5)
(i) A - B = [-3, 0]
(ii) A∩B =(0,5)
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