Statement 1: Sets { } and {0} are equal sets.
Statement 2: { } ≠ {0}.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Answer
Statement 1: { } is the empty set and contains no element, whereas {0} contains the element 0. So, { } and {0} are not equal. Hence, Statement 1 is false.
Statement 2: Since { } has no element and {0} has the element 0, the two sets are not equal, i.e. { } ≠ {0}. Hence, Statement 2 is true.
Hence, option 4 is the correct option.
Statement 1: Two sets A and B are overlapping if they have atleast one element in common.
Statement 2: If set A = { even natural numbers } and set B = { odd natural numbers }, sets A and B are disjoint.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Answer
Statement 1: By definition, two sets are overlapping if they have at least one element in common. Hence, Statement 1 is true.
Statement 2: A = { even natural numbers } and B = { odd natural numbers } have no element in common, so they are disjoint sets. Hence, Statement 2 is true.
Hence, option 1 is the correct option.