CAT Question > If P and Q be two sets such that P ∪ Q = P, ...

If P and Q be two sets such that P ∪ Q = P, then P ∩ Q will be:

Correct answer is 'Q'. Can you explain this answer?

Intersection

Let A and B be two sets. The intersection of A and B is the set of all those elements which are present in both sets A and B.

The intersection of A and B is denoted by A ∩ B

i.e., A ∩ B = {x : x ∈ A and x ∈ B}

The Venn diagram for intersection is as shown below:

Union:

Let A and B be two sets. The union of A and B is the set of all those elements which belong to either A or B or both A and B.

The union of A and B is denoted by A ∪ B.

i.e., A ∪ B = {x : x ∈ A or x ∈ B}

The Venn diagram for the union of any two sets is shown below:

A ∪ B = A + B - A ∩ B

As we know,

P ∪ Q = P + Q - P ∩ Q

Putting the values given in the question,

P = P + Q - P ∩ Q

P ∩ Q = Q

Hence, the correct answer is Q.

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If P and Q be two sets such that P ∪ Q = P, then P ∩ Q will be:Correct answer is 'Q'. Can you explain this answer? for CAT 2023 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If P and Q be two sets such that P ∪ Q = P, then P ∩ Q will be:Correct answer is 'Q'. Can you explain this answer? covers all topics & solutions for CAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If P and Q be two sets such that P ∪ Q = P, then P ∩ Q will be:Correct answer is 'Q'. Can you explain this answer?.

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IntersectionLet A and B be two sets. The intersection of A and B is the set of all those elements which are present in both sets A and B.The intersection of A and B is denoted by A ∩ Bi.e., A ∩ B = {x : x ∈ A and x ∈ B}The Venn diagram for intersection is as shown below:Union:Let A and B be two sets. The union of A and B is the set of all those elements which belong to either A or B or both A and B.The union of A and B is denoted by A ∪ B.i.e., A ∪ B = {x : x ∈ A or x ∈ B}The Venn diagram for the union of any two sets is shown below:A ∪ B = A + B - A ∩ BAs we know,P ∪ Q = P + Q - P ∩ QPutting the values given in the question,P = P + Q - P ∩ QP ∩ Q = QHence, the correct answer is Q.