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Tutor profile: Rooha A.

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Rooha A.
Academic Freelancer with 8+ years of teaching experience
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Questions

Subject: Set Theory

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Question:

Represent the following set in to Roaster form $$ A = \left \{ x: x \in N, x \leq 5\right \}$$

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Rooha A.
Answer:

The set A is given in Set Builder form. It has been mentioned that the elements are natural numbers and are less than or equal to 5. The natural numbers starts from 1 and counts up. So as per the definition of the given set, the numbers are 1,2,3,4, and 5. The roaster form of set representation starts with a open brace, all the elements listed with comma as separation between them and ends with a close brace as shown below. $$ A = \left \{ 1,2,3,4,5\right \}$$ So we can represent the set $$ A = \left \{ x: x \in N, x \leq 5\right \} = \left \{ 1,2,3,4,5\right \}$$

Subject: Electrical Engineering

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Question:

Optimize the logical expression for the function $$ f(A, B) = \sum(0, 2)$$ using Boolean algebraic laws

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Rooha A.
Answer:

The Boolean expression for the function can be written as $$f(A, B) = \sum (0, 2) = \overline{A}\cdot\overline{B} + A\cdot\overline{B} $$ We can see that the $$\overline{B}$$ is common in both product terms. So we can take $$\overline{B}$$ commonly outside of the bracket as given below. $$f(A, B) =\overline{B}\cdot(\overline{A}+A) \rightarrow (1)$$ We know that by complement rule of Boolean Algebra, the logical sum of a variable and it's complement is equal to logic 1 ($$\overline{A}+A = 1$$). So, we can modify the equation (1) as $$ f(A, B) =\overline{B}\cdot1 $$ $$ f(A, B) =\overline{B}$$ So the expression for the function f is optimized to $$ f(A, B) =\overline{B}$$.

Subject: Algebra

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Question:

Find the length and width of a rectangle whose perimeter is equal to 240 cm and its length is equal to twice its width.

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Rooha A.
Answer:

Let us assume the length of the rectangle be 'L' and the width of the rectangle be 'W'. The perimeter of a rectangle can be calculated from the Length and width using the following equation $$Perimeter = 2\times Length + 2\times Width$$ If we substitute the 'L' for length and 'W' for width, we get $$Perimeter = 2\times L + 2\times W.$$ The perimeter is given and the value is 240 cm. Substituting the value in the above equation, we get $$2\times L + 2\times W = 240cm$$ In the above equation, all terms are even. so we can divide both sides of the equation with 2. we get, $$L + W = 120cm \rightarrow (1)$$ It has been given that the length is twice the width,.i.e. $$ L = 2\times W \rightarrow (2)$$ Substituting value for W from equation (2) into equation (1), we get, $$ 2 \times W + W = 120cm $$ $$ 3 \times W = 120cm$$ or $$ W = 120\div 3 $$ $$ W = 40 cm $$ Substituting the value for W into equation (2), we get $$ L = 2 \times 40cm $$ $$ L = 80 cm $$. So, the length of the rectangle is found to be 80 cm and the width of the rectangle is 40 cm.

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