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Questions and Answers
What is the Boolean expression for the given logic circuit?
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?
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?
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}?
What is the geometric representation for {1, 3} x {-2, 3}?
Flashcards
Boolean Expression
Boolean Expression
An expression consisting of variables and logical operators, representing a logical statement.
Inverse Function Existence
Inverse Function Existence
A function has an inverse if and only if it is one-to-one (injective) and onto (surjective).
Cartesian Product
Cartesian Product
The Cartesian product of two sets creates a set of all possible ordered pairs, where the first element comes from the first set and the second element comes from the second set.
One-to-one Function
One-to-one Function
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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.
