DISCRETE MATH 2030 - TEST 2 REVIEW - QUESTIONS OFF QUIZ ONLY
Method of Direct Proof
1) Express statement as: ∀x ∈ D, if P(x) then Q(x) 2) Suppose x is a particular but random element of D (x ∈ D and P(x) ) 3) Find a way to show the conclusion Q(x) is true.
Write an informal negation for the following statements. Be careful to avoid negations that are ambiguous. Some estimates are accurate.
All estimates are inaccurate.
Write an informal negation for the following statements. Be careful to avoid negations that are ambiguous. Some suspicions were substantiated.
All suspicions were unsubstantiated
Fill in the blanks. A negation for "Some R have property S" is ___________________.
Fill in the blanks. A negation for "Some R have property S" is ___________________. A negation for "Some R have property S" is no R have property S.
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 _______________________.
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 _______________________. A statement of the form ∃x ∈ D such that Q(x) is true if , and only if, Q(x) is true for x is true for at least 1 elements of D.
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. If P(x) is a predicate with domain D, the truth set of P(x) is denoted _________. We read these symbols out loud as _______________________. If P(x) is a predicate with domain D, the truth set of P(x) is denoted {x ∈ d | P(x)}. We read these symbols out loud as the set of all x in D such that P(x).
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 the ones digit of x is 2, then the tens digit is 3 or 4.
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 the ones digit of x is 2, then the tens digit is 3 or 4. True ==> 3 || 4 is what the question asks.
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 the ones digit of x is 6, then the tens digit is 1 or 2.
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 the ones digit of x is 6, then the tens digit is 1 or 2. False. CounterExample is x = 36 ==> 1 || 2 is what the question asks.
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 < 0 then x is even.
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 < 0 then x is even. True
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 even then x ≤ 0.
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 even then x ≤ 0. False. CounterExample is x = -14
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 + {-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. True
Let D be the set of all students at UNO, and let M (s) be "s is a math major," let C (s) be "s is a computer science student," and let 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 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) be "s is a computer science student," and let 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 who is a math major. ∀s in D such that C (s) → E (s)
Let D be the set of all students at UNO, and let M (s) be "s is a math major," let C (s) be "s is a computer science student," and let 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). No computer science students is an engineering students.
Let D be the set of all students at UNO, and let M (s) be "s is a math major," let C (s) be "s is a computer science student," and let 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). No computer science students is an engineering students. ∀s in D such that C (s) → ~ E (s)
Let D be the set of all students at UNO, and let M (s) be "s is a math major," let C (s) be "s is a computer science student," and let 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). Some computer science students are also math majors.
Let D be the set of all students at UNO, and let M (s) be "s is a math major," let C (s) be "s is a computer science student," and let 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). Some computer science students are also math majors. ∃s in D such that C (s) ⋀ M (s)
Let D be the set of all students at UNO, and let M (s) be "s is a math major," let C (s) be "s is a computer science student," and let 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). Some computer science students are engineering students and some are not.
Let D be the set of all students at UNO, and let M (s) be "s is a math major," let C (s) be "s is a computer science student," and let 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). Some computer science students are engineering students and some are not. ∃s in D such that (C (s) ⋀ E (s)) ⋀ ∃s in D such that (C (s) ⋀ ~ E (s))
Let D be the set of all students at UNO, and let M (s) be "s is a math major," let C (s) be "s is a computer science student," and let 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) be "s is a computer science student," and let 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. ∃s in D such that E (s) ⋀ M (s)
Write an informal negation for the following statements. Be careful to avoid negations that are ambiguous. All dogs are friendly.
Some dogs are not friendly.
Write an informal negation for the following statements. Be careful to avoid negations that are ambiguous. All graphs are connected.
Some graphs are not connected.
Predicate
This is a form that has values with a finite number of possibilities that can become a statement when those values are substituted for real values
Write an informal negation for the following statements. 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.
Write an informal negation for the following statements. 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. Rewritten in formal would be --> ∀r, ∃s r + s = 1 ==> negated is ∃r, ∀s r + s ≠ 1. So, informal would be ===> There is some real number that when added together with any real number does not equal 1
