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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.
2. A low pressure area implies a coming stormconverse, inverse and contra positive
Number plates in an Arab country consist of 3 letters (chosen from a specified set of 20 letters from the Arabic alphabet) and 4 digits (from 0 to 9).
Find the probability of a plate having identical letters.
Find the probability of a plate having identical digits.
a. Determine the sets A and B, if A − B = {1, 2, 7, 8}, B − A = {3, 4, 10} and A ∩ B
= {5, 6, 9}.
b. Verify A ∪ (A ∩ B) = A using the rules of set algebra
6.
A multiple-choice test contains 10 questions. There are four possible answers for each question. b) In
how many ways can a student answer the questions on the test if the student can leave answers
blank?
The relation R on the set A={1,2,3,4,5}is defined by the rule (a,b) €R if 3|a-b|
