Educational

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8} then the universal set of all the three sets A, B and C can be…. Solution \[ A = \{1,3,5\} \] \[ B = \{2,4,6\} \] \[ C = \{0,2,4,6,8\} \] The universal set […]

For all sets A and B, B – (A ∩ B) is equal to…… Solution \[ B – (A \cap B) \] \[ = B \cap (A \cap B)’ \] \[ = B \cap (A’ \cup B’) \] \[ = (B \cap A’) \cup (B \cap B’) \] \[ = B \cap A’ \] \[

For all sets A and B, A – (A ∩ B) is equal to ….. Solution \[ A – (A \cap B) \] \[ = A \cap (A \cap B)’ \] \[ = A \cap (A’ \cup B’) \] \[ = (A \cap A’) \cup (A \cap B’) \] \[ = \Phi \cup (A \cap

When A = Φ, then the number of elements in P(P(A)) is ____________ Given: \[ A = \Phi \] Since the empty set has no elements, \[ n(A)=0 \] Therefore, \[ n(P(A)) = 2^0 = 1 \] Now, \(P(A)\) has 1 element. So the number of elements in \(P(P(A))\) is: \[ n(P(P(A))) = 2^1 =

The power set of set A = {1, 2} is ………. Given set: \[ A = \{1,2\} \] The power set of a set is the collection of all possible subsets of the set. Subsets of \(A\) are: \[ \Phi,\ \{1\},\ \{2\},\ \{1,2\} \] Therefore, the power set of \(A\) is: \[ P(A) = \{\Phi,\{1\},\{2\},\{1,2\}\}

When A = Φ then the number of elements in P(A) is ___________ Given: \[ A = \Phi \] The empty set contains no elements. Therefore, \[ n(A) = 0 \] The number of elements in the power set of a set having \(n\) elements is: \[ 2^n \] So, \[ n(P(A)) = 2^0 =

If A and B are any two sets, then A – B is equal to ___________ The difference of two sets means the set of elements which belong to set A but do not belong to set B. Using set identities: \[ A – B = A \cap B’ \] where \(B’\) represents the complement

If A and B are finite sets such that A ⊂ B, then n(A ∪ B) = _____________ Given: \[ A \subset B \] This means every element of set \(A\) is already present in set \(B\). Therefore, \[ A \cup B = B \] Taking cardinal numbers on both sides: \[ n(A \cup B)

The set {x ∈ R : 1 ≤ x < 2} can be written as ______________ Given set: \[ \{x \in \mathbb{R} : 1 \le x < 2\} \] This means: 1 is included in the set 2 is not included in the set Hence, in interval notation, the set is written as: \[ [1,2)

If A is a finite set containing n elements then the number of subsets of A is ____________ Let a finite set A contain n elements. The total number of subsets of a set having n elements is given by: \[ 2^n \] This includes: The empty set \((\emptyset)\) The set itself Answer \[ \boxed{2^n}