a) Suppose that ε is some fixed positive number. Use absolute value to rewrite the statement...
a) Suppose that ε is some fixed positive number.
Use absolute value to rewrite the statement
- There is some rational number x within
ε of √2
b) What is the negation of the statement above?
Homework Answers
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a) Suppose that ε is some fixed positive number.
Use absolute value to rewrite the statement...
Absolute value is always... 1. Positive 2. Non-negative Every fraction is a rational number. True or...
Absolute value is always... 1. Positive 2. Non-negative Every fraction is a rational number. True or False? The sum of 2/3 and 5/7 is 7/10. True or False? The quotient of two fractions cannot be a whole number True or False? The set of whole numbers is a subset of the set of rational numbers. True or False? Which of these fractions is between 7/13 and 14/19 ? 1. a. 6/17 2. b. 9/16 3. c. 1/2 4. d. None...
positive, then r +y> V+y 10. If r and y are (a) Quantify this statement. (b)...
positive, then r +y> V+y 10. If r and y are (a) Quantify this statement. (b) Give a careful proof of this statement. (c) Suppose drop the condition that r andy be positive, but add the absolute value: we Show that this proposition is false. (d) What if we are more careful and write Jrl + lyl> Vr2 +y2. Is this now true? 11. Consider the statement: The sum of V2 and a rational number is irrational. (a) How should...
a. Define what it means for two logical statements to be equivalent b. If P and Q are two statements, show that the statement ( P) л (PvQ) is equivalent to the statement Q^ P c. Write the converse a...
a. Define what it means for two logical statements to be equivalent b. If P and Q are two statements, show that the statement ( P) л (PvQ) is equivalent to the statement Q^ P c. Write the converse and the contrapositive of the statement "If you earn an A in Math 52, then you understand modular arithmetic and you understand equivalence relations." Which of these d. Write the negation of the following statement in a way that changes the...
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0....
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0. ________(b) m, n in N, 5m 2n is in N. ________(c) x in R, if |x − 2| < 3, then |x| < 5. #8. For each statement, (i) write the statement in logical form with appropriate variables and quantifiers, (ii) write the negation in logical form, and (iii) write the negation in a clearly worded unambiguous English sentence....
Suppose that F is a a finite number q field with of euments. some m positive...
Suppose that F is a a finite number q field with of euments. some m positive 6 integer b.
16 pts) #4. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) A statement...
16 pts) #4. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) A statement is a sentence that is true. ________(b) In logic, p q refers to the "inclusive or, " true when either p or q or both are true. ________(c) The phrase "not p and not q" means "not both p and q." ________(d) The conditional statement p q is true if p is false. ________(e) The negation of p q is p ~q. #5....
Use the well-ordering principle of natural numbers to show that for any positive rational number x...
Use the well-ordering principle of natural numbers to show that for any positive rational number x ∈ Q, there exists a pair of integers a, b ∈ N such that x = a/b and the only common divisor of a and b is 1.
. Suppose the discrete random variable X represents the number of a-particles discharged in a fixed...
. Suppose the discrete random variable X represents the number of a-particles discharged in a fixed period of time from some radioactive source. Suppose the probability that r particles are discharged during this fixed period is given by -2(2), r=0, 1.2 . e P(X = z) = =0, 1, 2, . . . . What is the expected number of a-particles released during this period? Hint: First find what Σ000 e ' equals. To do this, look up the power...
Problem #4 Solve the initial value problem as follows: dy dy +4+ (4 x +y) Then determine the positive number r such that - -4.04. Round-off the value of this positive number x to FOUR figures an...
Problem #4 Solve the initial value problem as follows: dy dy +4+ (4 x +y) Then determine the positive number r such that - -4.04. Round-off the value of this positive number x to FOUR figures and present it below (12 points): your mumerical result for the ae ust be written here) Also, you must provide some intermediate results obtained by you while solving the problem above: 1) The substitution used to solve the differential equation is as follows (mark...
Use the Chain Rule and the fact that d (r)-L,o find the derivative of (b) Rewrite f(x) as a piecewise function not...
Use the Chain Rule and the fact that d (r)-L,o find the derivative of (b) Rewrite f(x) as a piecewise function not involving the absolute value function. (c) Find the first and second derivatives of f(x),using your piecewise function. (d) Would you want to find" without the function's piecewise representation? 2. A square and a triangle are to be cut from a piece of fabric 1 metre square, as shown Find the length which minimises the removed area ar
Use...
positive, then r +y> V+y 10. If r and y are (a) Quantify this statement. (b) Give a careful proof of this statement. (c) Suppose drop the condition that r andy be positive, but add the absolute value: we Show that this proposition is false. (d) What if we are more careful and write Jrl + lyl> Vr2 +y2. Is this now true? 11. Consider the statement: The sum of V2 and a rational number is irrational. (a) How should...
a. Define what it means for two logical statements to be equivalent b. If P and Q are two statements, show that the statement ( P) л (PvQ) is equivalent to the statement Q^ P c. Write the converse and the contrapositive of the statement "If you earn an A in Math 52, then you understand modular arithmetic and you understand equivalence relations." Which of these d. Write the negation of the following statement in a way that changes the...
Suppose that F is a a finite number q field with of euments. some m positive 6 integer b.
. Suppose the discrete random variable X represents the number of a-particles discharged in a fixed period of time from some radioactive source. Suppose the probability that r particles are discharged during this fixed period is given by -2(2), r=0, 1.2 . e P(X = z) = =0, 1, 2, . . . . What is the expected number of a-particles released during this period? Hint: First find what Σ000 e ' equals. To do this, look up the power...
Problem #4 Solve the initial value problem as follows: dy dy +4+ (4 x +y) Then determine the positive number r such that - -4.04. Round-off the value of this positive number x to FOUR figures and present it below (12 points): your mumerical result for the ae ust be written here) Also, you must provide some intermediate results obtained by you while solving the problem above: 1) The substitution used to solve the differential equation is as follows (mark...
Use the Chain Rule and the fact that d (r)-L,o find the derivative of (b) Rewrite f(x) as a piecewise function not involving the absolute value function. (c) Find the first and second derivatives of f(x),using your piecewise function. (d) Would you want to find" without the function's piecewise representation? 2. A square and a triangle are to be cut from a piece of fabric 1 metre square, as shown Find the length which minimises the removed area ar
Use...
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