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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

Divide in the indicated base.35√2245
Convert the numeral to a Hindu–Arabic numeral.34257
Write the Hindu-Arabic numerals in the numeration system. Assume the numerals given are in a base 5 numeration system.85
Divide in the indicated base.46√2106
Convert the numeral to a Hindu–Arabic numeral.A9412
Divide in the indicated base.67√4047
First convert each numeral to a Hindu€“ Arabic numeral and then perform the indicated operation. Finally, convert the answer back to a numeral in the original numeration system. +
Divide in the indicated base.37√21017
Convert 463 to a numeral in the base indicated.Base 2
Add in the base indicated. 1214 + 3224
Convert 463 to a numeral in the base indicated.Base 4
First convert each numeral to a Hindu€“ Arabic numeral and then perform the indicated operation. Finally, convert the answer back to a numeral in the original numeration system.
Convert 463 to a numeral in the base indicated.Base 5
Write the Hindu€“Arabic numerals in the base 4 numeration system.Suppose colors as indicated below represent numerals in a base 4 numeration system.10 3 = 1 = 2 %3D
Convert 463 to a numeral in the base indicated.base 8
Write the Hindu€“Arabic numerals in the base 4 numeration system.Suppose colors as indicated below represent numerals in a base 4 numeration system.15 3 = 1 = 2 %3D
Convert 463 to a numeral in the base indicated.Base 12
Write the Hindu€“Arabic numerals in the base 4 numeration system.Suppose colors as indicated below represent numerals in a base 4 numeration system.60 3 = 1 = 2 %3D
Convert 463 to a numeral in the base indicated.Base 16
There is an alternative method for changing a base 10 numeral to a different base. This method will be used to convert 328 to base 5. Dividing 328 by 5 gives a quotient of 65 and a remainder of 3.
(a) What is 04 equal to in base 10?(b) What is 14 equal to in base 10?(c) What is 24 equal to in base 10?(d) What is 34 equal to in base 10? (e) In general, if n is a digit less than the
(a) What is 102 equal to in base 10?(b) What is 108 equal to in base 10?(c) What is 1016 equal to in base 10?(d) What is 1032 equal to in base 10?(e) In general, for any base b, what is 10b
(a) What is 112 equal to in base 10?(b) What is 118 equal to in base 10?(c) What is 1116 equal to in base 10?(d) What is 1132 equal to in base 10?(e) In general, for any base b, what is 11b equal to
Find b if 111b = 43.
Add in the base indicated. 30245 + 40235
Write the numeral as a Hindu–Arabic numeral.ιζυξζ
(a) Use the numerals 0, 1, and 2 to write the first 20 numbers in the base 3 numeration system.(b) What is the next numeral after 2223?
The ASCII code used by most computers uses the last seven positions of an eight-bit byte to represent all the characters on a standard keyboard. How many different orderings of 0’s and 1’s (or
Perform the indicated operation.D16√FACE16
Consider the multiplication (a) Multiply the numerals in base 8.(b) Convert 4628 and 358 to base 10. (c) Multiply the base 10 numerals determined in part (b).(d) Convert the answer
Determine b, by trial and error, if 1304b = 204.
Suppose a base 4 place-value system has its digits represented by colors as follows:(a) Determine the value of in base 10.(b) Write 177 in the base 4 system using only the four colors given in
In a base 4 system, each of the four numerals is represented by one of the following colors:Determine the value of each color if the following addition is true in base 4.
Subtract in the base indicated. 17138 –1243g ,
Subtract in the base indicated. F6416 -2A316
Multiply in the base indicated. 4316 х 36
Multiply in the base indicated. 23214 X 34
Independence Day is in July and Labor Day is in September, if and only if Thanksgiving is in April.Determine the truth value for each simple statement. Then, using the truth values, determine the
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook~ p
Determine the truth value of the statement if(a) p is true, q is false, and r is true.(b) p is false, q is true, and r is true.(~ r ∧ ~ q ) ∧ (~ r ∨ ~ p)
Neither is the chili spicy nor is the sour cream cold.Write the statement in symbolic form.Letp: The chili is spicy.q: The sour cream is cold.
If Weezer is not on the radio, then Oly is working.Use the fact that p → q is equivalent to ~ p ∨ q to write an equivalent form of the given statement.
Some vitamins contain sugar. Write the negation of the statement.
Some pedestrians are in the crosswalk.Write the negation of the statement.
Use De Morgan’s laws to determine whether the two statements are equivalent.~ (~ p ∧ q), p ∧ ~ q
Use De Morgan’s laws to determine whether the two statements are equivalent.~ (p ∧ q), ~ p ∧ ~ q
Construct a truth table for the statement.~ p → (q ∧ r)
The hurricane did $400,000 worth of damage to DeSoto County.Whether the statement is a simple statement or a compound statement. If it is a compound statement, indicate whether it is a negation,
Some skunks are tame.Pepé is a skunk.∴ Pepé is not tame.Use an Euler diagram to determine whether the syllogism is valid or invalid.
The book was neither a novel nor an autobiography.Whether the statement is a simple statement or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction,
Bobby joined the Army and he got married.Whether the statement is a simple statement or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction,
Write each compound statement in words.p: The coffee is Maxwell House.q: The coffee is hot.r: The coffee is strong.(p ∨ ~ q) ∧ ~ r
Louis Armstrong did not play the drums.Whether the statement is a simple statement or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction,
(a) Write a symbolic statement that represents the circuit.(b) Construct a truth table to determine when the lightbulb will be on. That is, determine which switches must be open and which switches
Time will go backward if and only if you travel faster than the speed of light.Whether the statement is a simple statement or a compound statement. If it is a compound statement, indicate whether it
If you write a history report, then the life of Benjamin Banneker would be a good topic.Whether the statement is a simple statement or a compound statement. If it is a compound statement, indicate
Mr. Waters is teaching Topics in Mathematics during the spring semester.Whether the statement is a simple statement or a compound statement. If it is a compound statement, indicate whether it is a
Fill in the blanks with an appropriate word, phrase, or symbol(s).If the conditional statement is not a tautology, then the argument is a(n) _______ argument.
Use p, q, and r to write each symbolic statement in words.p: Phobos is a moon of Mars.q: Callisto is a moon of Jupiter.r: Rosalind is a moon of Uranus~ (p ∧ r ) ↔ ~ q
Fill in the blanks with an appropriate word, phrase, or symbol(s).(a) The negation is symbolized by∽and is read _______(b) The conjunction is symbolized by ^ and is read ________(c) The disjunction
(a) Write a symbolic statement that represents the circuit.(b) Construct a truth table to determine when the lightbulb will be on. That is, determine which switches must be open and which switches
Fill in the blanks with an appropriate word, phrase, or symbol(s).If the conditional statement is a tautology, then the argument is a(n) _________ argument.
Fill in the blanks with an appropriate word, phrase, or symbol(s).Given the conditional statement p → q, the converse of the conditional statement in symbolic form is __________
Fill in the blanks with an appropriate word, phrase, or symbol(s).The negation of the conditional statement ~ (p → q) is equivalent to the following conjunction statement: ______
Fill in the blanks with an appropriate word, phrase, or symbol(s).A compound statement that is always true is known as a(n) _________.
Some pine trees are not green.Write the negation of the statement.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A truth table for a compound statement with(a) One distinct simple statement will have _________ cases.(b) Two distinct simple
Fill in the blanks with an appropriate word, phrase, or symbol(s).The following Euler diagram represents the statement __________ A€™s are B€™s. B
Use p, q, and r to write each symbolic statement in words.p: Phobos is a moon of Mars.q: Callisto is a moon of Jupiter.r: Rosalind is a moon of Uranus (p ∨ ~ q) → r
Fill in the blanks with an appropriate word, phrase, or symbol(s).Words such as all, none(or no), and some are examples of ________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).Two circuits are equivalent if they have equivalent _________ statements.
Fill in the blanks with an appropriate word, phrase, or symbol(s).To determine the validity of an argument with two premises, construct a truth table for a conditional statement of the form [(premise
Fill in the blanks with an appropriate word, phrase, or symbol(s).An argument that is invalid is also known as a(n) __________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The conditional statement p → q is equivalent to the following disjunction statement:______
Fill in the blanks with an appropriate word, phrase, or symbol(s).The biconditional statement p ↔ q is _____ only when p and q have the same truth value.
Some women are presidents.Write the negation of the statement.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The disjunction p ∨ q is false only when both p and q are __________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).If an Euler diagram can be drawn in a way in which the conclusion does not necessarily follow from the premises, the syllogistic
Fill in the blanks with an appropriate word, phrase, or symbol(s).A statement that consists of two or more simple statements is called a(n) ________ statement.
Fill in the blanks with an appropriate word, phrase, or symbol(s).When a switch labeled as pis open, a switch labeled as p̅ is _________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).When the conclusion of an argument does not necessarily follow from the given set of premises it is a(n) _________ argument.
Fill in the blanks with an appropriate word, phrase, or symbol(s).(a) ~ (p ∧ q) is equivalent to _______.(b) ~ (p ∨ q) is equivalent to _______.
Fill in the blanks with an appropriate word, phrase, or symbol(s).In the conditional statement p → q,(a) The lower-case letter p represents the__________.(b) The lower-case letter q represents the
No pets are allowed in this park.Write the negation of the statement.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The conjunction p ∧ q is true only when both p and q are _______.
Fill in the blanks with an appropriate word, phrase, or symbol(s).If an Euler diagram can be drawn only in a way in which the conclusion necessarily follows from the premises, the syllogistic
Fill in the blanks with an appropriate word, phrase, or symbol(s).A statement that conveys only one idea is called a(n) ___________ statement.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A disjunction, ∨ is used to represent switches in a(n) __________ circuit.
Fill in the blanks with an appropriate word, phrase, or symbol(s).When the conclusion of an argument necessarily follows from the given set of premises it is a(n) __________ argument.
Fill in the blanks with an appropriate word, phrase, or symbol(s).Statements that have exactly the same truth values in the answer columns of their truth tables are called __________ statements.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The conditional statement p ↔ q is ________ only when p is true and q is false.
All Acuras are Hondas.Write the negation of the statement.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The negation, ~ p will always have the ________ truth value of p.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The validity of a syllogistic argument can be determined __________ using a(n) diagram.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A sentence that can be judged either true or false is called a(n) _____________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The following Euler diagram represents the statement ___________ A€™s are B€™s. U B.
Construct a truth table for the statement.p ∧ ~ p
Write each compound statement in words.p: The coffee is Maxwell House.q: The coffee is hot.r: The coffee is strong.q ∨ r
Fill in the blanks with an appropriate word, phrase, or symbol(s).A compound statement that is always false is known as a(n) _______.
Fill in the blanks with an appropriate word, phrase, or symbol(s).Given the conditional statement p → q, the inverse of the conditional statement in symbolic form is _________

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