A and B are any two non-empty sets and A is proper subset of B. If n(A) = 5, then the minimum possible value of n(A∆ B) is Solution Since \[ A \subset B \] therefore, \[ A \cap B = A \] and \[ A \Delta B = (A-B)\cup(B-A) \] But, \[ A-B=\Phi \] […]
If n(A∩B) = 5, n(A∩C) = 7 and n(A∩B∩C) = 3, then the minimum possible value of n(B∩C) is…. Solution \[ n(A \cap B)=5 \] \[ n(A \cap C)=7 \] \[ n(A \cap B \cap C)=3 \] Since \[ A \cap B \cap C \subseteq B \cap C \] therefore, \[ n(B \cap C) \ge
If A, B and C are three non-empty sets such that any two of them are disjoint, then \((A \cup B \cup C) \cap (A \cap B \cap C) = …..\) Solution Since any two sets are disjoint, \[ A \cap B = \Phi,\qquad B \cap C = \Phi,\qquad A \cap C = \Phi \]
If n(A∩B) = 10, n(B∩C) = 20 and n(A∩C) = 30, then the greater possible value of n(A ∩ B ∩ C) is….. Solution \[ n(A \cap B)=10 \] \[ n(B \cap C)=20 \] \[ n(A \cap C)=30 \] Since \[ A \cap B \cap C \subseteq A \cap B \] therefore, \[ n(A \cap
Let S = {x : x is a positive multiple of 3 less than 100}, P = {x : x is a prime number less than 20}, Then, n(S) + n(P) = _____ Solution \[ S = \{3,6,9,\ldots,99\} \] Number of multiples of 3 less than 100: \[ \frac{99}{3} = 33 \] Therefore, \[ n(S)=33
For any three sets A, B and C, (A∪B∪C) ∩ (A∩B’∩C’) ∩ C’ is equal to __________ Solution \[ (A \cup B \cup C) \cap (A \cap B’ \cap C’) \cap C’ \] \[ = (A \cap B’ \cap C’) \cap (A \cup B \cup C) \] Using distributive law, \[ = (A \cap B’
For any three sets A,B and C, (A∪B∪C) ∩ (A∩B’∩C’) ∩ C’ is equal to __________ Read More »
If A and B are two sets, then (A ∩ B’)’ ∪ (B ∩ C) is equal to _________ Solution \[ (A \cap B’)’ \cup (B \cap C) \] \[ = (A’ \cup B) \cup (B \cap C) \] \[ = A’ \cup [B \cup (B \cap C)] \] \[ = A’ \cup B \]
If A and B are two sets, then (A ∩ B’)’ ∪ (B ∩ C) is equal to _________ Read More »
For any three sets A, B and C, (A – B) ∩ (C – B) is equal to __________ Solution \[ (A – B) \cap (C – B) \] \[ = (A \cap B’) \cap (C \cap B’) \] \[ = A \cap C \cap B’ \] \[ = (A \cap C) – B \]
For any three sets A,B and C, (A – B) ∩ (C – B) is equal to __________ Read More »
For any three sets A, B and C, (A – B) – (B – C) is equal to __________ Solution \[ (A – B) – (B – C) \] \[ = (A \cap B’) – (B \cap C’) \] \[ = (A \cap B’) \cap (B \cap C’)’ \] \[ = (A \cap B’) \cap
For any three sets A, B and C, (A – B) – (B – C) is equal to __________ Read More »
For any two sets A and B, [B’ ∪ (B’ – A)]’ is equal to……. Solution \[ [B’ \cup (B’ – A)]’ \] Using \[ X – Y = X \cap Y’ \] \[ = [B’ \cup (B’ \cap A’)]’ \] Using absorption law, \[ B’ \cup (B’ \cap A’) = B’ \] Therefore, \[
For any two sets A and B, [B’ ∪ (B ‘- A)]’ is equal to……. Read More »