Q 1. let A = { 1,4,5,10, 12,14}, B = { 1,2,3,14,13 }, C ={10}, Find a- C×B b- A

Question

Q 1. let  A = { 1,4,5,10, 12,14}, B = { 1,2,3,14,13 }, C={10}, Find

a-     C×B

b-     AB

c-      B-A

Solution:

Q 2.

A - Find the inverse of f(x)=8x+4 on real numbers.

B - Show that f(x)=x+6 is a bijective function

C-    By using definition of Big-O Notation, show that x^3-3x is O(x^3)

Solution:

Q 3.  Let A = {a, b, c}, B = {x, y, z}, C = {r, s, t}. Let f: A B and g: B C be defined by: f = {(a, y)(b, x), (c, y)} and g = {(x, s), (y, t), (z, r)}.

Find:

a-     Composition function g f: A C;

b-     The range of f , and the codomain of f

Solution:

Q 4. Use the bubble sort method to sort {6, 4, 7, 2, 9}, with showing the lists obtained at each step.

Solution:

Q 5.

a-     Find the integer "a" , where    a53 (mod 13), -15 a 0 .

b-     List five integers that are congruent to 6 modulo 8.

c-      The value of the modular expression ( 5 +6 7 ) + ( 3 .6 5 )

Solution:

Q 6. Find g.c.d and l.c.m. of 56 and 66 and show that g.c.d(56,66)×l.c.m(56,66)=56×66.

Solution:

Explanation / Answer

One question at a time please -- Policy of Chegg

A = { 1,4,5,10, 12,14}, B = { 1,2,3,14,13 }, C={10}
a-
C×B = {10} × { 1,2,3,14,13 }
= {(10, 1), (10, 2), (10, 3), (10, 14), (10, 13)}
Every possible combination

b- AB
= { 1,4,5,10, 12,14} { 1,2,3,14,13 }
= {1, 2, 3, 4, 5, 10, 12, 13, 14}
Elements that are either in A or in B or in both

c- B-A
= { 1,2,3,14,13 } - { 1,4,5,10, 12,14}
= {2, 3, 13}
Elements that are in B but not in A

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