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Unit 1 – Set Theory and Logic – PRACTICE TEST1. For the following Sets? The universal set U = {natural numbers from 1 to 50 inclusive}? T = {multiples of 3}? N = {multiples of 9}? V = {multiples of 20}a) List all the elements from each set of T, N and V in the Universal Set b) Write each of the sets T, N, V and N in set notationc) Represent the sets in a Venn Diagram (write all the numbers into the diagram) d) List any subsets in Set Notation, list any disjoint sets, list any complimentary sets.f) Determine the following: n(U) = ____n(T’) = ____n(T∩N) = ____n(T∪N) = ____n(T) = ____n(N’) = ____n(T∩V) = ____n(T∪V) = ____n(N) = ____n(V’) = ____n(N∩V) = ____n(N∪V) = ____n(V) = ____n(T∪N∪V) ’ = ____n(T∩N∩V) = ____ n(N∪V∪T) = ____2. A school offers the following athletics for extra-curricular. They can be sorted into the following sets: Outdoor (O), Played with a ball (B), and Performed on a stage (S). Classify the following based on which set they belong to: Football _____Soccer _____Wrestling _____Basketball _____Cross Country _____Badminton _____Volleyball _____Golf _____Track and Field _____Cheer _____Curling _____Floor Hockey _____a) Draw a Venn Diagram that relates all the sets with the universal setting being all athletics offered in the school (A).b) Determine the number of elements in set A, O, B and Sc) Determine the union and intersection of O and B. Show using set notation listing the elements. d) Determine the union and intersection of B and S. Show using set notation listing the elements. e) Determine the union and intersection of O and S. Show using set notation listing the elements. f) Determine the number of elements in the union and intersection of O and B. Show using set notation. g) Determine the number of elements in the union and intersection of B and S. Show using set notation. h) Determine the number of elements in the union and intersection of O and S. Show using set notation. i) Describe any disjoint sets 3. You are playing a game where you roll a red six-sided dice and a black six-sided dice. You multiply the numbers in order to score points. Fill out the following outcome table to determine the possible products of numbers. The following sets can be made: Even (E), Odd (O), Doubles (D), Greater than Fifteen (G), Lower than Fifteen (L). 123456123456Determine the following: n(D∪E) = ____n(D∩E) = ____ n(E∪O) = ____ n(E∩O) = ____ n(D∪O) = ____n(D∩O) = ____ n(E∪G) = ____ n(E∩G) = ____ n(D∪G) = ____ n(D∩G) = ____ n(E∪L) = ____ n(E∩L) = ____ n(D∪L) = ____ n(D∩L) = ____ n(O∪G) = ____ n(O∩G) = ____ n(O∪L) = ____ n(O∩L) = ____ n(G∪L) = ____ n(G∩L) = ____** There could be a question that is also about a deck of cards. Go to Example 4 of Lesson 4 for more practice **REMEMBER: There are 52 cards, 13 of each suite (club, spade, heart, diamond), each suite has 10 number cards and 3 face cards.4. These nine attribute cards have three different shapes, numbers, and shadings (clear, striped, or solid). Each set of three cards must have:? the same number or three different numbers, and? the same shape or three different shapes, and? the same shading or three different shadings.All the cards can be used more than once.Determine four sets, with three cards in each set. Please draw out each set.5. Fully complete a Venn diagram and determine how many are in both set A and B. The universal set is 500:? 75 are in set A.? 94 are in set B. ? 350 are not in Set A or B. 6. Complete a fully Venn Diagram: The universal set is 261. ? Set A has 99? Set A and B has 22 ? 55 are not in A, B or C? Set B has 102? Set A and C has 15? Set C has 78? Set B and C has 267. When a number is divisible by 5 its final digit is 0. a) Write a conditional statement. Determine if it is true or false. If it is false, provide a counter example. b) Write the converse. Determine if it is true or false. If it is false, provide a counter example.c) Write the inverse. Determine if it is true or false. If it is false, provide a counter example.d) Write the contrapositive. Determine if it is true or false. If it is false, provide a counter example.e) Is this statement bi-conditional. 8. Determine if the following conditional statement is bi-conditional: If an animal is a giraffe, then it has a long neck. 28135421062500360218332510005802923692780059787747478400 ................
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