MATH 092 Lecture Notes - Lecture 5: Sentence Clause Structure, Ampersand, Associative Property

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oliverabbit203

18 Aug 2016

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Document Summary

A statement is a sentence which is true or false as it stands. "4 + 3 = 5" are, respectively, true and false mathematical statements. Many sentences occurring in mathematics contain variables and are therefore not true or false as they stand, but become statements when the variables are given values. Simple examples are "x < 4", "x < 1/", "x is an integer", "3x2 + y2 = 10". If p(x) is a frame containing the one variable "x", then p(5) is the statement obtained by replacing "x" in p(x) by the numeral "5". For example, if p(x) is "x < 4", then p(5) is "5 < 4", p(0) is "0 < 4", and so on. Another way to obtain a statement from the frame p(x) is to assert that p(x) is always true. We do this by prefixing the phrase "for every x".

Related Questions

5. (18 pts) Circle True if the statement is ALWAYS true; circle False otherwise. No explanations are required. Let f be a one-to-one function and f its inverse. (a) If the point (2, 5) lies on the graph off, then the point (5,2) lies on the graph of f. True False f (2) = 5 f-1 (5) = 2 (b) sin-1 (T) = 0 True False Since >1, ris not in the domain of sin-?; | or sin-1 (7) #0, since sin (0) = 0 # Iff and g are two functions defined on (-1, 1), and if (c) limg (x) = 0, then it must be true that lim[ f(x) g (x)] = 0. True False Let f (x) = 1 / x, if x #0, and f (0) = 4 and g(x) = x. Then lim g (x) = lim (x) = 0, but Lim ( f (x) g(x)] = lim [() x] = 18 0. Iffis continuous on (-1, 1), and if f (0) = 10 and lim g (x) = 2, (a) True False then lin (= 5. Because lim : (*) - Limx-of (*) .f(0) = 20 = 5 If f is continuous on [1, 3], and if f(1) = 0 and f(3) = 4, then the equation f(x) = (e) has a solution in (1, 3). True False Since f continuous on [1, 3), f(1) = 0 < < 4 = f (3), by the Intermidiate Value Theorem there exists a cin (1, 3) such that f (c) = . (f) Let f be a positive function with vertical asymptote x = 5. Then lim f (x) = +0. True False Let f (x) = 1, if x < 5, and f (x) ==, ifx>5. Then lim f (x) = +00, and therefore, X = 5 is a vertical asymptote. 5 - X So, f is a positive function with vertical asymptote x = 5 but lim f (x) + +co, since lim f (x) = + 0 + lim f (x) = 1, which means that lim f (x) does not exist.

Equations and Inequalities

Equations: True or False?

Independent Practice

1. Consider the statement: 4 - 3 + 5 = -6 + 8 + 4. This is a mathematically correct sentence.

Is the sentence true or false? Explain how you know.

2. Determine if the sentence is true. Select all that apply.

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3. Determine whether the following number sentences are TRUE or FALSE. Justify your answer.

4. For the equation, x-7=24, can a value be substituted for x to make that a true number sentence? How many values could be substituted for x and have a true number sentence?

5. Consider x+4=x+8 . What values could be substituted for x to make this a true number sentence? Explain how you know.

6. Determine what value(s) for the variable would make each algebraic equation a true number sentence.

is true for _______________.