Questions with Complete Solutions - Hamro CSIT

Explain fuzzy set with example. How do you find complement of a fuzzy set?

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What is congurent modulo? Determine whether 37 is congurent to 3 modulo 7 and wheather -29 is congurent to 5 modulo 17.

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Define network flow with example. What are saturated edge, unsaturated edge and slack value?

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Give an example of tautology and contradiction. Show that implication and contrapositive are equivalence.

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What is direct proof ? Give a direct proof that if m and n are both perfect squares, then mn is also a perfect square.

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What is product rule? How many strings are there of four lowercase letters that have the letter x in them?

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Explain the matrix representation of relations with example.

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Define function. Let f₁ and f₂ be function from R to R such that f₁(x) = x² and f₂(x) = x – x² . What are the functions f₁ + f₂ and f₁ . f₂?

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Explain linear homogeneous recurrence relation with constant coefficients. What is the solution of the recurrence relation a_n = 6a_n-1 – 9a_n-2 with initial conditions a₀ = 1 and a₁ = 6?

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Let us assume tha R be a relation on the set of ordered pair of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Is R an equivalence relation?

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