Discrete Mathematics Quiz for MCA and BCA Students
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Questions and Answers

What is the Boolean expression for the given logic circuit?

  • $(p ar{q} ar{r}) ar{}$
  • $(p ar{q} ar{r}) + (p q r)$
  • $(p ar{q} r) + (p q ar{r})$ (correct)
  • $(p + q + r)$
  • If $f: ext{R} o ext{R}$ is a function given by $f(x) = x^3 - 2$, does $f^{-1}$ exist?

  • No, $f^{-1}$ does not exist
  • Not enough information to determine
  • It is indeterminate
  • Yes, $f^{-1}$ exists (correct)
  • How many words can be formed using the letters of the word ‘DEPARTMENT’, if each letter must be used at most once?

  • 3628800
  • 40320 (correct)
  • 72576
  • 181440
  • What is the geometric representation for {1, 3} x {-2, 3}?

    <p>A rectangle</p> Signup and view all the answers

    Study Notes

    Logic Circuit

    • No specific information provided about the logic circuit, hence Boolean expression cannot be determined.

    Function Invertibility

    • The function $f: \mathbb{R} \to \mathbb{R}$ is given by $f(x) = x^3 - 2$.
    • To determine if $f^{-1}$ exists, we need to check if the function is injective (one-to-one) and surjective (onto).
    • Since $f(x) = x^3 - 2$ is a cubic function, it is bijective, hence $f^{-1}$ exists.

    Word Formation

    • The word is 'DEPARTMENT'.
    • We need to form words using each letter at most once.
    • The number of words that can be formed is not specified, but it's a permutation problem (arrangement of letters).

    Geometric Representation

    • The given sets are {1, 3} and {-2, 3}.
    • The geometric representation is not explicitly stated, but it is likely a Cartesian product or a set of points in a coordinate plane.

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    Description

    Test your understanding of Discrete Mathematics with this quiz. Topics include truth tables, logical equivalences, mathematical induction, and more. Ideal for students of MCA and BCA programs.

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