A committee is to be selected from 5 candidates a, b, c, d and e. The selection must satisfy all the following conditions : • Either a or b must be included, but not both • Either c or e or both must be included • If d is included then b must be included • Either a or c are included or neither is included. • If e is included, then c and d must be included. How should selection be made ?
\(a \land \bar{b} \land c \land \bar{d} \land \bar{e}\)
\(a \land \bar{b} \land c \land \bar{d} \land \bar{e}\) option is correct.
Encode the constraints as boolean rules on the five candidates: \((a \oplus b) \land (c \lor e) \land (d \Rightarrow b) \land (a \Leftrightarrow c) \land (e \Rightarrow (c \land d))\).
Step 1 — assume \(a = 1\); by \(a \Leftrightarrow c\) we get \(c = 1\). Then \(a \oplus b\) forces \(b = 0\), so \(d \Rightarrow b\) forces \(d = 0\), and \(e \Rightarrow (c \land d)\) forces \(e = 0\). So \((a, \lnot b, c, \lnot d, \lnot e)\) satisfies every rule.
Step 2 — the alternative branch \(a = 0\) forces \(b = 1\) and \(c = 0\); then \(c \lor e\) demands \(e = 1\), but \(e \Rightarrow c\) contradicts \(c = 0\). The a-in branch is the only consistent assignment.
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.................... is a client server application that identifies each host on the internet with a unique user-friendly name.
Every OS has a ................ or .......... which primarily resides in the main memory of the computer to perform some of the basic functions of the OS.
(i) Kernel
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(i) Machine language
(ii) Assembly language
(iii) High level language
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Which part of the QR code represents the encoded data?
