Question: Approximate the following numbers: a) \(\sqrt {51} \) b) \(\tan 46 ^ {0} \). Answer a) Follow the formula: \(f (x_ {0} + \Delta x) \approx f (x_ {0}) + f '(x_ {0}) \Delta x \). > Consider the function \(f (x) = \sqrt {x}, f '(x) = \frac {1} {2 \sqrt {x}}, x_ {0} = 49, \Delta x = 2 \) we get: \(\sqrt {51} = \sqrt {49 + 2} \approx \sqrt {49} + \frac {1} {2 … [Read more...] about Approximate the following numbers: a) \(\sqrt {51} \) b) \(\tan 46 ^ {0} \).

## Prove that the following clauses are logically equivalent: $ (A \wedge B) \Rightarrow C; \bar C \Rightarrow (\bar A \vee \bar B) $

Question: Prove that the following clauses are logically equivalent: $ (A \wedge B) \Rightarrow C; \bar C \Rightarrow (\bar A \vee \bar B) $ Answer We prove that: $ \left ({A \wedge B} \right) \Rightarrow C = \bar C \Rightarrow \left ({\bar A \vee \bar B} \right) $ We have: $ \left ({\overline {A \wedge B}} \right) \Rightarrow C = \bar C \Rightarrow \left ({\bar A … [Read more...] about Prove that the following clauses are logically equivalent: $ (A \wedge B) \Rightarrow C; \bar C \Rightarrow (\bar A \vee \bar B) $

## 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} = k + (k + 1) + ... + (k + m - 1) $ (1) For $ k, m \in N, k \ge 1, m \ge 2 $ We have: $ \begin { array} {l} (1) … [Read more...] about Prove that it is impossible to represent the number $ 2 ^ n, n \in N $, the sum of two or more consecutive natural numbers.

## Please specify the set of all subsets of the set {$ 1, 2, 3, 4 $}.

Question: Please specify the set of all subsets of the set {$ 1, 2, 3, 4 $}. Answer This set has $ 2 ^ 4 = 16 $ subsets, that is: $ \emptyset $, $ \left \{{1} \right \} $, $ \left \{{2} \right \} $, $ \left \{{3} \right \} $, $ \left \{{4} \right \} $ $ \left \{{1; 2} \right \} $, $ \left \{{1; 3} \right \} $, $ \left \{{1; 4} \right \} $, $ \left \{{2; 3} \right \} … [Read more...] about Please specify the set of all subsets of the set {$ 1, 2, 3, 4 $}.

## In one exam, Tran Quy Cap school had 12 students won prizes in which: $ 7 $ students won at least two prizes, $ 4 $ students won at least $ 3 $ prizes; $ 2 $ students won the most prize, each $ 4 $ prize. How many awards have A school won?

Question: In one exam, Tran Quy Cap school had 12 students won prizes in which: $ 7 $ students won at least two prizes, $ 4 $ students won at least $ 3 $ prizes; $ 2 $ students won the most prize, each $ 4 $ prize. How many awards have A school won? Answer Call $ A, B, C, D $ in turn is a combination of students who won $ 4 $ prize, at least $ 3 $ prize, at least $ 2 … [Read more...] about In one exam, Tran Quy Cap school had 12 students won prizes in which: $ 7 $ students won at least two prizes, $ 4 $ students won at least $ 3 $ prizes; $ 2 $ students won the most prize, each $ 4 $ prize. How many awards have A school won?