Ministry of Food
Post: Sub-Assistant Engineer
Exam Date: 09/02/2021, Exam Taker: BPSC
1) Set, Power Set, Proper Subset
Set: A set is a well-defined collection of distinct objects (elements).
Example: A = {1, 2, 3}
Power Set: The power set of A, written P(A), is the set of all subsets of A.
Example: If A = {1,2}, then P(A) = {∅, {1}, {2}, {1,2}}
Proper Subset: A is a proper subset of B (A ⊂ B) if every element of A is in B and A ≠ B.
Example: {1,2} ⊂ {1,2,3}
2) Membership Table Proof
Prove: overline{A ∪ (B ∩ C)} = (C’ ∪ B’) ∩ A’
Conclusion: The column overline{A∪(B∩C)} and the column (C’∪B’)∩A’ are identical for all 8 cases. Hence, the identity is proved.
1) Set, Power set, Proper subset
Set: Set হলো কিছু নির্দিষ্ট (well-defined) আলাদা আলাদা element-এর collection।
Example: A = {1, 2, 3}
Power set: কোনো set A-এর power set P(A) হলো A-এর সব subset-এর set।
Example: A = {1,2} হলে P(A) = {∅, {1}, {2}, {1,2}}
Proper subset: A হলো B-এর proper subset (A ⊂ B) যদি A-এর সব element B-তে থাকে এবং A ≠ B হয়।
Example: {1,2} ⊂ {1,2,3}
2) Membership table দিয়ে প্রমাণ
প্রমাণ কর: overline{A ∪ (B ∩ C)} = (C’ ∪ B’) ∩ A’
Conclusion: সব ৮টি case-এ overline{A∪(B∩C)} কলাম এবং (C’∪B’)∩A’ কলাম একদম একই। তাই identity প্রমাণিত।
Given:
A − B = {1, 5, 7, 8}
B − A = {2, 10}
A ∩ B = {3, 6, 9}
Concept Used
A set can be reconstructed using:
A = (A − B) ∪ (A ∩ B)
B = (B − A) ∪ (A ∩ B)
Finding Set A
A = {1, 5, 7, 8} ∪ {3, 6, 9}
A = {1, 3, 5, 6, 7, 8, 9}
Finding Set B
B = {2, 10} ∪ {3, 6, 9}
B = {2, 3, 6, 9, 10}
Final Answer
A = {1, 3, 5, 6, 7, 8, 9}
B = {2, 3, 6, 9, 10}
Diagram of Combinational and sequential circuit:
A’B’C’ + B’CD’ +A’BCD’+ AB’C’
=A’B’C’D’+A’B’C’D+A’B’CD’+AB’CD’++A’BCD’+AB’C’D’+AB’C’D
MINTERM(0,1,2,6,8,9,10)
