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379.

A logical binary relation ζ , is defined as follows:

A B
AζB

True True True

True False True

False True False

False
False True

Let ~be the unary negation (NOT) operator, with higher precedence then ζ.
Which one of the following is equivalent to A Λ B? [2 marks]
(A) (~ A ζB)
(B) ~ (Aζ~ B)
(C) ~ (~ Aζ ~ B)
(D) ~ (~ A ζ B)

asked in Computer Science And Engineering, 2006

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380.

Consider the following propositional statements:

Which one of the following is true? [2 marks]
(A) P1 is a tautology, but not P2
(B) P2 is a tautology, but not P1
(C) P1 and P2 are both tautologies
(D) Both P1 and P2 are not tautologies

asked in Computer Science And Engineering, 2006

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381.

Which one of the first order predicate calculus statements given below correctly expresses the following English statement?
Tigers and lions attack if they are hungry or threatened. [2 marks]

asked in Computer Science And Engineering, 2006

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382.

Let S = {1,2,3,........,m},m > 3. Let X₁...... X_n be subsets of S each of size 3. Define a function f from S to the set of natural numbers as, f (i ) is the number of sets X_j that contain the element i. That is f(i) = |{j | i ∈ X_j|}|.
, [2 marks]
(A) 3m
(B) 3n
(C) 2m + 1
(D) 2n + 1

asked in Computer Science And Engineering, 2006

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383.

Given a set of elements N = {1,2,.....,n} and two arbitrary subsets A ⊂ N and B ⊂N,how many of the n! permutations π from N to N satisfy min(π (A)) = min(π (B)),where min(S) is the smallest integer in the set of integers S, and π(S) is the set of integers obtained by applying permutation π to each element of S ? [2 marks]
(a) (n − |A U B| ) |A| |B|
(b) (|A|² + |B|²) n²
(c) n!|A∩B|/|A∪B|
(d) |A∩B|²/ {n/(A∪B)}

asked in Computer Science And Engineering, 2006

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384.

F is an n × n real matrix. b is an n ×1 real vector. Suppose there are two n ×1vectors, u and v such that u ≠ v , and Fu = b, Fv = b. Which one of the following statements is false? [2 marks]
(A) Determinant of F is zero
(B) There are an infinite number of solutions to Fx = b
(C) There is an x ≠ 0 such that Fx = 0
(D) F must have two identical rows

asked in Computer Science And Engineering, 2006

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