Exercise: 5-D
Mental Maths
Q1: Fill in the blanks:
i. If \(A \subseteq B\) and \(B \subseteq A\), then ______.
Answer: \(A = B\)
ii. If \(A = \{1, 2, 3\}\) and \(B = \{1, 2, 3, 4\}\), then \(A – B =\) _______.
Answer: \(\phi\) (empty set)
iii. If \(\xi = \{a, b, c, d, e, f\}\) and \(A = \{b, d, e\}\), then \(A’ =\) ______.
Answer: \(\{a, c, f\}\)
iv. \(x \in A \cup B,\ \Rightarrow x \in A\) ______ \(x \in B\).
Answer: or
v. If A is a subset of B, then B is a _______ of A.
Answer: superset
vi. The set of all possible subsets of a set is called its ________.
Answer: power set
Q2: Write true (T) or false (F):
i. Set of all persons on earth is an infinite set.
Answer: False (It is a finite set)
ii. \(\{x : x + 4 = 4\}\) is a singleton set.
Answer: True (Only \(x=0\) satisfies the condition)
iii. The power set of a set containing 3 elements, has 6 elements.
Answer: False (Power set has \(2^3 = 8\) elements)
iv. Two sets A and B are said to be equal if \(n(A) = n(B)\).
Answer: False (Equal sets must have same elements, not just same number of elements)
v. Equal sets are always equivalent.
Answer: True (Equal sets have same elements, so they are equivalent)
vi. The minimum number of subsets a non-empty set has is 2.
Answer: True (Every non-empty set has at least \(\phi\) and itself as subsets)
