Assertion (A): {2, 4, 6, ....} and {1, 3, 5, ....} are equivalent sets.
Reason (R): {2, 4, 6, .....} has an infinite number of elements and {1, 3, 5, ......} also has an infinite number of elements.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Answer
Assertion (A): {2, 4, 6, ....} is the set of even natural numbers and {1, 3, 5, ....} is the set of odd natural numbers. Both are infinite sets, and two infinite sets are always equivalent. So, Assertion (A) is true.
Reason (R): Both {2, 4, 6, .....} and {1, 3, 5, ......} have an infinite number of elements. So, Reason (R) is true, and it correctly explains the Assertion.
Hence, option 3 is the correct option.
Assertion (A): Sets A and B are equal if all elements of A are in B and all elements of B are in A.
Reason (R): If two sets have identical elements, they are equal.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Answer
Assertion (A): Two sets are equal if all elements of A are in B and all elements of B are in A, i.e. the two sets have identical elements. So, Assertion (A) is true.
Reason (R): If two sets have identical elements, they are equal. This is the definition of equal sets, so Reason (R) is true, and it correctly explains the Assertion.
Hence, option 3 is the correct option.