two finite sets a and b are such that a subset to b then which of the following is not correct??
a. aub=b b.anb=a c.a-b={} d.b-a={}
Answers
Answer:
b-a= {} is the Correct Answer
Step-by-step explanation:
Because when two finite sets are subset then All other options except d is right.
Two Sets are said to be finite if the elements are countable and two sets are said to be subset when two sets are Equal, they are also Equivalent! Set A is a Subset of Set B if every element in Set A is also in Set B. It is written as ⊆.
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Question: Two finite sets A and B are such that A is a subset of B then which of the following is not correct?
a. A∪B = B b. A∩B = A c. A - B = { }
d. B - A = { }
Answer:
The answer is option (c).
Step-by-step explanation:
Subset: A set A is said to be a subset of a set B if every element of A is also an element of B.
Mathematically, A⊂B if a ∈ A, then a ∈ B.
According to the question,
It is given that the sets A and B are finite such that A⊂B.
a. A∪B = B
Since A⊂B.
Then by the definition of subset, every element of A is also an element of B.
⇒ A∪B = B
Thus, option (a) is correct.
b. A∩B = A
Since A⊂B.
Then the common elements of the sets A and B are the elements of set A.
⇒ A∩B = A
Thus, option (b) is correct.
c. A - B = { }
Since A⊂B.
⇒ Set A is smaller than set B.
So, the set A - B is the set that contains the elements of A only which is not possible.
Thus, option (c) is incorrect.
d. B - A = { }
It is possible that the set B - A is empty if and only if A⊆B.
Thus, option (d) is correct.
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