Assume that 0 and 1 are considered as Boolean constants and A, B, C are…
2026
Assume that 0 and 1 are considered as Boolean constants and A, B, C are Boolean variables. Answer the following questions based on Boolean Logic, where:
"+" (plus sign) represents the OR operation
"." (dot sign) represents the AND operation
" ' " (apostrophe) represents the NOT (Complement/Inverter) operation
(A) Write the name of the Boolean Law represented by the following expression:
(A.B)' = A' + B'
(B) Simplify the following Boolean expression using appropriate Boolean laws:
A + A.B'
(C) Given that A XOR B' = C, where XOR represents the XOR operator, evaluate the value of the following expression:
A' XOR B
(D) Name any one Universal Logic Gate used in Boolean Logic.
Attempted by 63 students.
Show answer & explanation
(A) The law is De Morgan’s Law: (A.B)' = A' + B'. It states that complement of AND becomes OR of complements.
(B) A + A.B' = A (using Absorption Law: A + A.X = A).
(C) Given A ⊕ B' = C. Using XOR property: A' ⊕ B = (A ⊕ B') = C. Hence, value = C.
(D) One Universal Gate: NAND Gate (can implement all logic functions).
Example/Diagram (De Morgan):
(A.B)' → NOT of AND
Equivalent: A' + B' → OR of NOT
Conclusion: Boolean laws simplify expressions and reduce circuit complexity.