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Let $A$ be the set of all prime numbers, $B$ be the set of all even prime numbers, and $C$ be the set of all odd prime numbers. Consider the following three statements in this regard:

  1. $A=B\cup C$.
  2. $B$ is a singleton set
  3. $A = C \cup \{2\}$

Then which one of the following holds?

  1. None of the above statements is true.
  2. Exactly one of the above statements is true.
  3. Exactly two of the above statements are true.
  4. All the above three statements are true.
in Set Theory & Algebra
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1 Answer

1 vote
A={2,3,5,7,11,13,17,19........}

B={2}    ($\because$ 2 is the only even prime.Because,if any other prime is divisible by 2, then it is not prime)

C={3,5,7,11,13,17,19,23....} ($\because$all primes except 2 are odd.)

1-True.It can be clearly seen that $A= B \cup C$

2-True.Since,B has only 1 element.

3-True .$\because$ C need only one element 2 to become A.

$\therefore$all the statements are true.

Hence option D

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