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How to find total no. of unordered pairs of disjoint subsets of a finite set? Solution) Suppose A and B are two such disjoint subsets of the set S. Then every element can go into A or B or the set S (3 choices). We only require to exclude the possibility of all elements choosing to be in S itself. Therefore the number of ways is 3n-1
Q. Subtraction Involving Negative Numbers? In order to subtract positive and negative numbers, you need to be aware of the Rule for Subtraction. This rule states that subtracti
Let R be the relation on S = {1, 3, 6, 9, 27} defined by aRb iff a|b. (a) Write down the matrix of R. (b) Draw the digraph of R. (c) Explain whether R is reflexive, irrere
Prove the subsequent Boolean expression: (x∨y) ∧ (x∨~y) ∧ (~x∨z) = x∧z Ans: In the following expression, LHS is equal to: (x∨y)∧(x∨ ~y)∧(~x ∨ z) = [x∧(x∨ ~y)] ∨ [y∧(x∨
what is number of quadratic equation that are unchanged by squaring their roots is There are four such cases x 2 =0 root 0 (x-1) 2 =0 root 1 x(x+1)=0 roots 0 and 1
Integration by Parts -Integration Techniques Let's start off along with this section with a couple of integrals that we should previously be able to do to get us started. Fir
Consider the following interpolation problem: Find a quadratic polynomial p(x) such that p(x0) = y0 p’(x1) = y’1 , p(x2) = y2 where x0 is different from x2 and y0, y’1 , y2 a
1. Using given data set (Assignment_1data in the folder) a) Make scatterplot between "Years since first marriage" and "Total children ever born" b) Make scatterplot between
The square of one integer is 55 less than the square of the next consecutive integer. Find the lesser integer. Let x = the lesser integer and let x + 1 = the greater integer. T
Evaluate following integrals. (a) ∫ 3e x + 5 cos x -10 sec 2 x dx (b) ( 23/ (y 2 + 1) + 6 csc y cot y + 9/ y dy Solution (a) ∫ 3e x + 5 cos x -10 sec 2 x
What is Dividing Fractions? If you want to divide two fractions, you invert the second fraction (that is, turn it upside-down) and change the division sign to a multiplication
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