DISCRETE MATH 2030 - FINAL TEST 4 REVIEW (W/ TESTS 1 - 3 ONLY)

Fill in the blanks.The contrapositive of "if p then q" is ________________________. :

DEFINE: A STATEMENT : THIS IS A SENTENCE THAT IS EITHER TRUE OR FALSE, BUT IT CAN'T BE BOTH

Write the statements in symbolic form using the symbols ~, V, and ^ and the indicated letters to represent component statements. Leth = "John is healthy"w = "John is wealthy"s = "John is wise*John is neither healthy, wealthy, nor wise. : ~h ^ ~ w ^ ~ s

Write the statements in symbolic form using the symbols ~, V, and ^ and the indicated letters to represent component statements. Leth = "John is healthy"w = "John is wealthy"s = "John is wise*John is neither wealthy nor wise, but he is healthy. : (~w ^ ~s) ^ h

Fill in the blanks.The negation of "if p then q" is _______________________. :

Fill in the blanks.A condition statement and its contrapositive are ____________________________. :

DETERMINE WHETHER THE STATEMENT FORMS(~p V q) V (p ^ ~q)Is a tautology. Construct a truth table and include a few words of explanation to justify your answer. :

Write the negation, contrapositive, converse, and inverse for the following statement. (Assume that all variables represent fixed quantities or entities, as appropriate)"If today is New Years' Eve, then tomorrow is January." : Negation: Today is New Year's Eve and tomorrow is not January.Contrapositive: If tomorrow is not January, then today is not New Year's Eve.Converse: If tomorrow is January, then today is New Year's Eve.cInverse: If today is not New Year's Eve, then tomorrow is not January.

Fill in the blanks using a variable or variables to rewrite the statement. "There is a real number whose product with every real number equals zero."There is a real number a such that the product of a _________________________________________. :

Fill in the blanks using a variable or variables to rewrite the statement. "There is a real number whose product with every real number equals zero."There is a real number a with the property that for every real number b, _________________. :

Write an informal negation for the following statement. Be careful to avoid negations that are ambiguous.Given any real number, a real number can be found so that the sum of the two equals 1. (re-written -> ∀r, ∃s r+s = 1 (formal) ∃r, ∀s r+s ≠ 1) :

Let D = {-48, -14, -8, 0, 1, 3, 16, 23, 26, 32, 36}. Determine which of the following statements are true and which are false. Provide a counter example for the statement that are false.∀x ∈ D, if x is odd the x > 0. :

Let D be the set of all students at UNO, and let M(s) be "s is a math major," let C(s) b "s is a computer science student," and le E(s) be "s is an engineering student." Express each of the following statements using quantifiers, variables, and the predicates M(s), C(s), and E(s)."There is an engineering student who is a math major." :

Let D be the set of all students at UNO, and let M(s) be "s is a math major," let C(s) b "s is a computer science student," and le E(s) be "s is an engineering student." Express each of the following statements using quantifiers, variables, and the predicates M(s), C(s), and E(s)."Every computer science student is an engineering student." :

Fill in the blanks.If P(x) is a predicate with domain D, the truth set of P(x) is denoted _____________. We read these symbols out loud as ___________________. :

Fill in the blanks.A statement of the form ∃x ∈ D such that Q(x) is true if, and only if, Q(x) is _______ for __________________. :

Write an informal negation for each of the following statements. Be careful to avoid negations that are ambiguous.The product of any even integer and any odd integer is even. :

Consider the statement "∃x such that ∀y, P(x, y), a property involving x and y, is true." A negation for this statement is: :

Fill in the Blanks.The most common way to disprove a universal statement is to find ______________. :

Fill in the Blanks.According to the method of generalizing from the generic particular, to show that every element of a set satisfies a certain property, suppose x is a ___________________________, and show that _________________. :

Suppose b is any integer. If b mod 12 = 5, what is 7b mod 12? :

If today is Monday, what day of the week will it be 1,000 days from today? :

Fill in the blanks:The triangle inequality says that for all real numbers x and y, _______________. :

The divisibility by a prime theorem says that every integer greater than 1 is _______________________. :

Show that √2 is irrational. :

Show that for every real number x, if x − ⌊x⌋ ≥ 1/2 then ⌊2x⌋ = 2⌊x⌋ + 1. :