UC Davis‚ ECS 20‚ Winter 2014 Instructor: Vladimir Filkov Midterm Review Exercises 1. Write the truth table for the proposition (r q) (p r). q Ans: p q) (p r) r (r p T T T T F F F F 2. T T F F T T F F T F T F T F T F T T F T T F F F Find a proposition with three variables p‚ q‚ and r that is true when exactly one of the three variables is true‚ and false otherwise Ans: (p q r) (p q r) (p q r). 3
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number that is not an integer)‚ 8.6 (a rational number expressed in decimal representation)‚ and π (3.1415926535...‚ an irrational number). As a subset of the real numbers‚ the integers‚ such as 5‚ express discrete rather than continuous quantities. Complex numbers include real numbers as a special case. Real numbers can be divided into rational numbers‚ such as 42 and −23/129‚ and irrational numbers‚ such as pi and the square root of two. A real number can be given by an infinite decimal representation
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1. Introduction of the lesson. 2. Questioning 3. Explanation 4. Stimulus Variation 5. Black Board Writing. UNIT-VI a) Number System : Natural Number‚ Whole Number‚ Integers‚ Rational Number‚ Irrational Number and Operations with Numbers. b) Polynomial. c) Equations: Linear‚ Simultaneous and Quadratic Equations and their solution. d)
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number. On the other hand‚ the square root of 8‚ does not come out even‚ when calculated through a calculator‚ the answer is 2.828427125‚ an irrational number. The exact values of these irrational numbers cannot be expressed in decimal form‚ and must be left in radical form because the decimal values are rounded and not completely accurate. These irrational radical numbers are called surds. Surds can also be represented in series. In mathematics‚ given an infinite sequence of numbers (an )‚ a series
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Questions: 1] Which of the following is irrational: [Marks:1] A. B. C. D. 2] Find the value of p such that (x -1) is the factor of the polynomial x3+10x2+ px . [Marks:1] A. p = 7 B. p = -7 C. p = 11 D. p = -11 3] Find remainder when is divided by [Marks:1] A. -1 B. 1 C. 2 D. Zero 4] What are the two factors of quadratic polynomial ? [Marks:1] A. (x+8) and (x-8) B. (x+16) and (x-4) C. (x-16) and (x-64) D. (x-8) and (x-8) 5] Given
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written as a fraction and as such these are both subsets of rational numbers. Irrational Numbers Numbers that cannot be written as a fraction are called irrational. Example √2‚ √5‚ √7‚ Π. These numbers cannot be written as a fraction so they are irrational. Surds A surd is any number that looks like this √21‚ √15‚ √17. A surd is a root that cannot be written exactly as a decimal or a fraction. They are irrational. Simplifying Surds A surd can be simplified by rewriting the number inside
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Although all of Theodorus’ work has been lost‚ Plato put Theodorus into his dialogue Theaetetus‚ which tells the reader of his achievements. It is assumed that Theodorus had proved that all of the square roots of non-square integers from 3 to 17 are irrational by means of the Spiral of Theodorus.[2] Plato quoted Theaetetus speaking to Socrates: It was about the nature of roots. Theodorus was describing them to us and showing that the third root and the fifth root‚ represented by the sides of squares
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government‚ and feature different kinds of repressive social control systems. A lack or absence of individual freedoms and expressions are common within the genre‚ as is warfare and violence. BioShock is a first-person shooter video game developed by Irrational Games (at the time‚ named 2K Boston)‚ and published by 2K Games. Bioshock fits the description of what one would typically expect from a dystopic body of work. In dystopian visions articulated at the beginning of the twenty-first century‚ one can
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MATHS-SA1-TEST1 Q1) Use the following information to answer the next question. The steps for finding the H.C.F. of 2940 and 12348 by Euclid’s division lemma are as follows. 12348 = a × 4 + b a = b × 5 + 0 What are the respective values of a and b? A. 2352 and 588 B. 2940 and 588 C. 2352 and 468 D. 2940 and 468 Answer The steps to find the H.C.F. of 12348 and 2940 are as follows. 12348 = 2940 × 4 + 588 2940 = 588 × 5 + 0 Comparing with the given steps‚ we obtain a =
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shack with a corrugated tin roof‚ in that elusive‚ irrational number with which scientists try to understand the universe‚ I found refuge." (1.5.41) This name is important because of its scientific significance. Pi is an irrational number. Pi like and enjoys math and science. The fact that this number is irrational gives and elusive effect whereas the fact that it goes
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