MTH299 Final Exam Review 1. Describe the elements
... 4. Suppose that A, B, and C are sets. Which of the following statements is true for all sets A, B, and C? For each, either prove the statement or give a counterexample: (A ∩ B) ∪ C = A ∩ (B ∪ C), A ∩ B ⊆ A ∪ B, if A ⊂ B then A × A ⊂ A × B, A ∩ B ∩ C = A ∪ B ∪ C. ...
... 4. Suppose that A, B, and C are sets. Which of the following statements is true for all sets A, B, and C? For each, either prove the statement or give a counterexample: (A ∩ B) ∪ C = A ∩ (B ∪ C), A ∩ B ⊆ A ∪ B, if A ⊂ B then A × A ⊂ A × B, A ∩ B ∩ C = A ∪ B ∪ C. ...
Course Outline PDF file
... Verify, by substitution, that the values determined in solving a radical equation algebraically are roots of the equation. Explain why some roots determined in solving a radical equation algebraically are ...
... Verify, by substitution, that the values determined in solving a radical equation algebraically are roots of the equation. Explain why some roots determined in solving a radical equation algebraically are ...
McCallum ch 08
... (a) The equation 2x2 = a is equivalent to x2 = a/2, which has no solutions if a is negative, and has the solution x a / 2 if a ≥ 0, so Range = all a such that a ≥ 0. We can see this from the graph of y = 2x2 in Figure 8.7. There is a point on the graph corresponding to every non-negative y-value. ...
... (a) The equation 2x2 = a is equivalent to x2 = a/2, which has no solutions if a is negative, and has the solution x a / 2 if a ≥ 0, so Range = all a such that a ≥ 0. We can see this from the graph of y = 2x2 in Figure 8.7. There is a point on the graph corresponding to every non-negative y-value. ...
2-3 weeks - Community Unit School District 200
... one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibiliti ...
... one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibiliti ...
1 Polynomial functions
... essentially by hand. As a result enormous amounts of thought and energy went into the task of figuring out how to approximate other functions with polynomials. Trigonometric and exponential/logarithmic functions occur very naturally, but how does one calculate with them? We approximate with polynomi ...
... essentially by hand. As a result enormous amounts of thought and energy went into the task of figuring out how to approximate other functions with polynomials. Trigonometric and exponential/logarithmic functions occur very naturally, but how does one calculate with them? We approximate with polynomi ...
Propositional Logic What is logic? Propositions Negation
... • Essentially, logic formalizes our reasoning process. – It provides a common language through which we can demonstrate to each other that our reasoning is valid. ...
... • Essentially, logic formalizes our reasoning process. – It provides a common language through which we can demonstrate to each other that our reasoning is valid. ...
