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Construct a formal proof which shows that the sentence below is a theorem of predicate logic. *the E's are existential quantifiers (usually designated by backwards E's). the & are "and". Do not use quantifier negation rules.
[(x)(~Rx or Nx)& ~(Ex)Nx or (Ey)(z)Szy] ->(~(Ex)Rx or (z)(Ey)Szy
Use Gram-Schmidt algorithm to the sequence {x_1,x_2, x_3} to find an orthonormal basis of S. Use the result above to find the QR factorization of the matrix A=(x_1l x_2l x_3).
How many different trains of white (1x1) and/or red (1x2) rods are there of a given length N? Find at least 2 ways to justify your solution
If the graph of a function has three x intercepts, then it must have at least two points at whch its tangent line is horizontal. If f'(x) = 0 for all x in the domain of f, then f is a constant function.
Suppose A divides N and B divides N. Does this always imply: A * B divides n? Now the question is under what condition A*B will always divide N? Prove it.
Pronet has annual sales of $724 million from its 600 retail stores. Pronet can reduce its mail float by 2 days through the use of wire transfers. The annual cost of the wire transfers is expected to be $105,610.
Suppose that f is continuous on [a,b]. Prove that f is integrable, i.e., ( the integral symbol with b at top and a at the bottom) f exists.
Find the slope and the y-intercept of the line represented by the equation: 2x + y = 14. Write the equation of a line in slope-intercept form with the slope of -4/5 and y-intercept (0, -3)
Probability of drawing the following card. One card is drawn from an ordinary deck of 52 cards. Find the probability of drawing the following card
Probability: Working with the standard distribution curve. A company installs 5000 light bulbs, each with an average life of 500 hours and a standard deviation of 100 hours, and a distribution approximated by a normal curve
Determine whether the given ordered pair is a solution of the system. Solve each system by substitution method
Determine whether A=B , if A is a subset of set B, if set B is a subset is a subset of A, if set A is a proper subset of set B, if set B is a proper subset of set A , or if none of these applies.
Probability of guessing four correct out 20 multiple choices, If a student randomly guesses at 20 multiple-choice questions, what is the probability that the student gets exactly four correct?
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