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Questions and Answers
What is the inverse of the function defined by the simple cipher function $f(x) = 3x - 4$?
What is the inverse of the function defined by the simple cipher function $f(x) = 3x - 4$?
- $f^{-1}(x) = \frac{x + 4}{3}$ (correct)
- $f^{-1}(x) = \frac{x - 4}{3}$
- $f^{-1}(x) = 3x + 4$
- $f^{-1}(x) = 3(x - 4)$
For the power set of the set $X = {a, b, c, d}$, how many elements does the power set have?
For the power set of the set $X = {a, b, c, d}$, how many elements does the power set have?
- 16 (correct)
- 4
- 12
- 8
If 60 students are surveyed, with 40 liking math and 36 liking science, how many students like either math or science?
If 60 students are surveyed, with 40 liking math and 36 liking science, how many students like either math or science?
- 28
- 52 (correct)
- 60
- 44
Which statement correctly defines the relation $R = {(a, b) \mid a \text{ divides } b}$ on the set $A = {1, 2, 3, 4, 6, 8, 12, 24}$?
Which statement correctly defines the relation $R = {(a, b) \mid a \text{ divides } b}$ on the set $A = {1, 2, 3, 4, 6, 8, 12, 24}$?
What is the total family income if a salesperson and his son both sell Rupees 1,50,000 worth of merchandise?
What is the total family income if a salesperson and his son both sell Rupees 1,50,000 worth of merchandise?
Flashcards
Inverse Function
Inverse Function
The inverse of a function f(x) swaps the input (x) and output (y) values, resulting in a new function f⁻¹(x).
Partially Ordered Set (Poset)
Partially Ordered Set (Poset)
A set with a relationship that is reflexive, antisymmetric, and transitive, allowing comparison of elements.
Hasse Diagram
Hasse Diagram
A graphical representation of a poset, highlighting the ordering relationships between elements.
Divisibility Relation
Divisibility Relation
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Venn Diagram
Venn Diagram
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Function Composition
Function Composition
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Equivalence Relation
Equivalence Relation
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Symmetrical Property about y=x
Symmetrical Property about y=x
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Boolean Function
Boolean Function
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Composition of functions
Composition of functions
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Study Notes
Simple Cipher Function
- A simple cipher codes a number using the function f(x) = 3x - 4
- Find the inverse function
- Determine if the inverse is a function
- Verify symmetrical property about the line y = x
POSet Definition
- Define POSet (Partially Ordered Set)
- Show that (X, ≤) is a POSet
- X = {a, b, c} (example set)
- Draw the Hasse diagram for the power set of X
More POSet Examples
- Define POSet
- Show (X, ≤) is a POSet, where X = {a, b, c, d}
- Draw Hasse diagram for the power set of X
Relation as POSet
- Let A = {2, 3, 6, 12, 24, 36}
- Relation R = {(a, b) | a divides b}
- Show (A, R) is a POSet
- Draw the Hasse diagram
Another Relation as POSet
- Let A = {1, 2, 3, 4, 6, 8, 12, 24}
- Relation R = {(a, b) | a divides b}
- Show (A, R) is a POSet
- Draw the Hasse diagram
Student Survey
- 60 students total
- 40 like math
- 36 like science
- 24 like both math and science
- Calculate students who like:
- Math only
- Science only
- Either math or science
- Neither math nor science
Salesperson Earnings
- Salesperson's annual earnings: A(x) = 30,000 + 0.04x
- Son's annual earnings: S(x) = 25,000 + 0.05x
- x = rupee value of merchandise
- Find (A + S)(x)
- Calculate total family income if they each sell ₹1,50,00,000 worth of merchandise
Equivalence Relation
- Define Equivalence relation
- Show that R = {(x, y) | x² = y²} is an equivalence relation on S = ℝ
Function Composition
- f(x) = x²
- g(x) = 3x
- h(x) = x²
- Prove (fog) o h = f o (go h)
Boolean Functions
- Write Boolean function for Boolean variables {0, 1}
- F(x, y) = xy
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