Question: Prove that the following clause is a true constant clause: $ (p \wedge (p \Rightarrow q)) \Rightarrow q $ Answer Based on the formulas: $ \begin {array} {l} p \Rightarrow q \equiv \bar p \vee q \\ p \wedge q \equiv \bar p \vee \bar q \\ \bar p \Rightarrow \bar q \equiv p …
Q&A Mathematics
[QAZ] ALGEBRA PRACTICE TEST 3
MATH PLACEMENT PRACTICE TEST – ALGEBRA PRACTICE TEST 3 1. Simplify the expression (4x+22x)/(2x) A 6 B 2+2x C 2×2x D 2x+1 2. Simplify the expression (2×2-5x-12)/(2×2-4x-16). A (x-6)/2(x-2) B (x-6)/2(x+2) C (2x+3)/2(x-2) D (2x+3)/2(x+2) 3. Suppose that the function f(x) is a quadratic function with roots at x=2-3i and x=2+3i. Find f(x). A f(x)=x2-4x-5 B f(x)=x2-4x+13 C f(x)=x2-6ix-5 D f(x)=x2-6ix+13 4. Solve the inequality for x. …
[QAZ] Prove that the following clause is a true constant clause: $ p \Rightarrow (q \Rightarrow p) $
Question: Prove that the following clause is a true constant clause: $ p \Rightarrow (q \Rightarrow p) $ Answer Based on the formulas: $ \begin {array} {l} p \Rightarrow q \equiv \bar p \vee q \\ p \wedge q \equiv \bar p \vee \bar q \\ \bar p \Rightarrow \bar q \equiv p \wedge bar …
[QAZ] Prove that the following clause is a true constant clause: $ p \Rightarrow (p \vee q) $
Question: Prove that the following clause is a true constant clause: $ p \Rightarrow (p \vee q) $ Answer Based on the formulas: $ \begin {array} {l} p \Rightarrow q \equiv \bar p \vee q \\ p \wedge q \equiv \bar p \vee \bar q \\ \bar p \Rightarrow \bar q \equiv p \wedge bar …
[QAZ] Give $ A = [1, 4]; B = (2, 6); C = (1, 2) $. Find $ A \cap B \cap C $.
Question: Give $ A = [1, 4]; B = (2, 6); C = (1, 2) $. Find $ A \cap B \cap C $. Answer Recall: $ x \in A \cap B \cap C \Leftrightarrow \begin {cases} x \in A \\x \in B \\x \in C \end {cases} $ We need to find the numbers …
[QAZ] Give $ A = [1, 4]; B = (2, 6); C = (1, 2) $. Find $ A \cap B \cap C $.Read More
[QAZ] ALGEBRA PRACTICE TEST 4
MATH PLACEMENT PRACTICE TEST – ALGEBRA PRACTICE TEST 4 1. (2a2b – 3c3)(3a3b + 4c) = 5a6b2 + 12c4 – 9a3bc3 – 12c4 5a5b2 + 8a2bc – 9a3bc3 + 12c4 6a5b2 + 8a2bc – 9a3bc3 + 12c4 6a6b2 + 8a2bc – 9a3bc3 – 12c4 6a5b2 + 8a2bc – 9a3bc3 – 12c4 2. Which equation is represented by the graph shown below? 5a6b2 + 12c4 – 9a3bc3 – 12c4 5a5b2 + …
[QAZ] Prove that there is no largest prime number. (or: Prove that the set of primes is an infinite set)
Question: Prove that there is no largest prime number. (or: Prove that the set of primes is an infinite set) Answer Assuming $ {P_n} $ is the largest prime number, we call p the product of n known prime numbers: $ \begin {array} {l} p = {p_1} {p_2} .. .. {p_n} \\ \end {array} $ …
[QAZ] Important 2D and 3D Geometric Shapes and Figures
Important 2D and 3D Geometric Shapes and Figures 2D ============= 3D
[QAZ] Important 2D and 3D Geometric Shapes and FiguresRead More
[QAZ] Prove that it is impossible to represent the number $ 2 ^ n, n \in N $, the sum of two or more consecutive natural numbers.
Question: Prove that it is impossible to represent the number $ 2 ^ n, n \in N $, the sum of two or more consecutive natural numbers. Answer Suppose we can express the number $ {2 ^ n}, n \in N $ into the sum of m consecutive natural numbers: $ {2 ^ n} = …
[QAZ] [Video] All trigonometry formulas and Tricks to Understand Trigonometry Formulas
All trigonometry formulas and Tricks to Understand Trigonometry Formulas ======== 1) Six trigonometric ratios 2) Inverse Trigonometric Ratios 3) Value Table for Standard Angles 4) Complementary Angles 5) Trigonometric Identities 6) Application of Trigonometry 7) Horizontal Level 8) Line of Sight 9) Angle of Elevation 10) Angle of Depression ============== ============ Exact Trigonometry Values – …
[QAZ] [Video] All trigonometry formulas and Tricks to Understand Trigonometry FormulasRead More