Assertion (A) : The set of all prime numbers less than 30 is {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
Reason (R) : Every repeated element in a set is taken only once.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
Answer
The prime numbers less than 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. So, the given set is correct.
Thus, Assertion (A) is true.
Every repeated element in a set is indeed taken only once.
Thus, Reason (R) is true.
However, listing the distinct prime numbers less than 30 does not involve any repetition, so Reason (R) does not explain Assertion (A).
Hence, option 2 is the correct option.
Assertion (A) : If A = {1, 2, 3, 4, 5, 6} and B = {a, b, c, d, e, f}, then A and B are equivalent sets.
Reason (R) : Two sets A and B are said to be equivalent if every element of A is in B and every element of B is in A.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
Answer
A = {1, 2, 3, 4, 5, 6} and B = {a, b, c, d, e, f}, so n(A) = n(B) = 6. Since they have the same cardinal number, A and B are equivalent sets.
Thus, Assertion (A) is true.
The condition "every element of A is in B and every element of B is in A" is the definition of equal sets, not equivalent sets. Two sets are equivalent when n(A) = n(B).
Thus, Reason (R) is false.
Hence, option 3 is the correct option.