Question

EXERCISE 2.4 1. Given $1 = {3,6,9, 52 = (a, b), and S3 = {m, n}, find the Cartesian products: (0) Sy x 52 (b) $2 x S3 (C) 53 x 51 5. If the domain of the function y=5+ 3x is the set (* 1<x< 9), find the range of the function and express it as a set. EXERCISE 2.3 3. Referring to the four sets given in Prob. 2, find: (a) S, US (c) S2 S3 () 54 525 (b) SU SE (d) S2 S4 ( 53 U SU 54 4. Which of the following statements are valid? (a) AUA = A (d) ALU = U (9) The complement of (b) An A = A (e) A=0 A is A. AU=A (1) ANU = A S. Given A = (4,5,6}, B = {3,4,6,7), and C = 2, 3, 6), verify the distributive law. 8. Enumerate all the subsets of the set S= {a,b,c,d). How many subsets are there altogether? EXERCISE 2.5 1. Graph the functions (a) y = 16 + 2x (b) y = 8 - 2x (C) y = 2x + 12 (In each case, consider the domain as consisting of nonnegative real numbers only.) 3. Graph the functions (a) y = -x2 + 5x - 2 (b) y = x2 + 5x – 2 with the set of values -5<x<5 constituting the domain. It is well known that the sign of the coefficient of the x2 term determines whether the graph of a quadratic func- tion will have a "hill" or a "valley." On the basis of the present problem, which sign is associated with the hill? Supply an intuitive explanation for this. 4. Graph the function y = 36'x, assuming that x and y can take positive values only. Next, suppose that both variables can take negative values as well; how must the graph be modified to reflect this change in assumption? 5. Condense the following expressions: (b) x x x xx (C) x3 x y3 x 23 6. Find: (a) x3/x-3 (b) (x1/2 x X1/3)/x2/3 (a) *4 x 815

Answer 1

1) A) |S₁ x S₂| = |S₁|.|S₂| = 3.2 = 6 and the six distinct product can be written as = {(3,a)(3,b)(6,a)(6,b)(9,a)(9,b) }

B) |S₂ x S₃| = |S₂| . |S₃| = 2.2 = 4 and the four distict product can be written as ={(a,m)(a,n)(b,m)(b,n)}

C) |S₃ x S₁| = |S₃| . |S₁| = 2.3 = 6 and the six distinct product can be written as = {(m,3)(m,6)(m,9)(n,3)(n,6)(n,9)}

5) y = 5 + 3x and domain is {1,2,3,4,5,6,7,8,9}

Than range set will be given as =

Range set = { 8 , 11 , 14 ,17 , 20 , 23 , 26 , 29 , 32 }

Here is the solution for first 2 questions.

As per HOMEWORKLIB RULES we are permitted to do the only first question in multiple questions untill learner don't ask any specific question.

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