BPSC (Multiple Ministry) Assistant Programmer (ICT) — Exam: 19.07.2023প্রশ্ন ও সমাধান

Direct answer. De Morgan's theorem gives two rules for pushing a NOT through an AND or an OR, converting one into the other:

• First law: (A . B)' = A' + B' — the complement of an AND is the OR of the complements.
• Second law: (A + B)' = A' . B' — the complement of an OR is the AND of the complements.

Proof by truth table (first law):

A	B	A.B	(A.B)'	A'	B'	A'+B'
0	0	0	1	1	1	1
0	1	0	1	1	0	1
1	0	0	1	0	1	1
1	1	1	0	0	0	0

Columns (A.B)' and A'+B' match in every row, confirming the law.

Everyday example: "It is NOT (raining AND cold)" is logically the same as "It is NOT raining OR NOT cold."

Gate-level equivalence: a NAND gate behaves exactly like a negative-input OR gate (an OR gate whose inputs are first individually inverted); a NOR gate behaves like a negative-input AND gate.

graph LR
  A1((A)) --> N{NAND}
  B1((B)) --> N
  N --> O1[Output]
  A2((A)) --> T1{NOT}
  B2((B)) --> T2{NOT}
  T1 --> R1{OR}
  T2 --> R1
  R1 --> O2[Same output as NAND]

This equivalence is the basis for redrawing any AND/OR/NOT circuit using only NAND (or only NOR) gates, since both are functionally complete gate sets.

Boolean simplification example: simplify F = (A' + B)' + C

• Apply De Morgan to (A'+B)': (A'+B)' = A.B' (De Morgan's 2nd law)
• F = A.B' + C (no further simplification possible)

Exam takeaway: De Morgan's laws let you convert freely between AND/OR forms — essential for simplifying Boolean expressions and for implementing any logic function using a single gate type (NAND-only or NOR-only design).

Direct answer. ACID is the set of four properties that guarantee a database transaction is processed reliably: Atomicity, Consistency, Isolation, Durability.

Property	Meaning	Bank-transfer example (500 from Account A to B)
Atomicity	The transaction is "all or nothing" — either every step commits, or none do.	If the debit from A succeeds but the credit to B fails (e.g. power loss), the entire transaction is rolled back — A is never left short with nothing credited to B.
Consistency	The database moves from one valid state to another, preserving all defined rules/constraints.	Total money across A and B before and after the transfer is identical — no money is created or destroyed.
Isolation	Concurrent transactions do not interfere with each other's intermediate (uncommitted) state.	A second transaction reading A's balance mid-transfer never sees a "half-debited" value.
Durability	Once committed, changes survive any subsequent failure (crash, power loss).	After the transfer is confirmed, even an immediate server crash cannot undo the completed transfer.

Why it matters: without ACID guarantees, concurrent access and system failures could silently corrupt data (money vanishing, duplicate charges) — ACID is the contract that lets applications trust the database under real-world faults and concurrency.

Exam takeaway: ACID = Atomicity (all-or-nothing), Consistency (valid state to valid state), Isolation (concurrent transactions don't see each other's half-finished work), Durability (committed = permanent) — the standard reliability guarantee of relational (and many modern) database systems.