Discrete Mathematics Answers

1.5 Solve the equation below using Inverse method (10 marks)

"\\begin{bmatrix}\n 1 & 3 & 0 \\\\\n 0 & 0.5 & 1\\\\\n0.05 & 0 & 1\\\\\n\n \\end{bmatrix}" "\\begin{bmatrix}\n x \\\\\n y\\\\\nz\\\\\n\\end{bmatrix}" ="\\begin{bmatrix}\n 4 \\\\\n 1\\\\\n3\\\\\n\\end{bmatrix}"

Using a Truth table, determine the value of the compound proposition(10marks)

((𝑝 ∨ 𝑞) ∧ (￢𝑝 ∨ 𝑟)) → (𝑞 ∨ 𝑟).

How many positive integers less than 1000 have at least one decimal digit equal to 9?

Find a recurrence relation for the number of bit sequences of length n with an odd number of 0s?

In a class 100 students how much minimum number of students is there whose first name begin with the same alphabet

Translate each of these quantifications into English language and determine its truth

value.

1. ∃x∈R (x3 = −1)

2. ∀x∈Z (x2 ∈ Z)

Use existential and universal quantifiers to express the

statement "Everyone has exactly two biological parents"

using the propositional function P(x, y), which represents

"x is the biological parent of y."

Express this statement using quantifiers: "Every student

in this class has taken some course in every department

in the school of mathematical sciences."

Let P(n) be the statement that n! < nn, where n is an in- teger greater than 1.

Translate in two ways each of these statements into logical expressions using predicates, quantifiers, and logical connectives. First, let the domain consist of the students in your class and second, let it consist of all people. a) Everyone in your class has a cellular phone. b) Somebody in your class has seen a foreign movie. c) There is a person in your class who cannot swim. d) All students in your class can solve quadratic equations. e) Some student in your class does not want to be rich.