Design a security access circuit where access is granted

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Reference no: EM134002641

Computational Mathematics

Question 1: Mathematical Argumentation & Proof Techniques

(a) Prove by mathematical induction:
n! + (n - 1)! + (n - 2)! = n2 (n - 2)! for all n ≥ 2

(b) A recursive file compression algorithm processes n files where processing time:

T(n) = T(n - 1) + (n - 2)!

The base case T(2) = 2 holds. Prove by induction that:

T(n) = n2 (n - 2)!

Question 2: Logic Application & Digital Circuits
(a) Construct truth tables for:
i. ¬p ∨ ¬q
ii. p ∧ (q ∨ r)

(b) Design a security access circuit where access is granted if both keycard (P) AND PIN (Q) are valid, OR emergency override (R) is active.
Draw the circuit and truth table. No AI shortcuts — Get genuine assignment help from experienced, real tutors.

Question 3: Predicate Logic & Rules of Inference

(a) Translate to predicate logic (P(x) = person, S(x) = sleeping):
i. Someone is sleeping
ii. No one is sleeping
iii. Everyone is sleeping

(b) Student database query: "Some student is cheating on exam" (C(x) = cheating).
Translate its negation and determine if "All students are honest" logically follows.

Reference no: EM134002641

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