4 Questions
What is the Boolean expression for the given logic circuit?
$(p ar{q} r) + (p q ar{r})$
If $f: ext{R} o ext{R}$ is a function given by $f(x) = x^3 - 2$, does $f^{-1}$ exist?
Yes, $f^{-1}$ exists
How many words can be formed using the letters of the word ‘DEPARTMENT’, if each letter must be used at most once?
40320
What is the geometric representation for {1, 3} x {-2, 3}?
A rectangle
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.
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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