Let A = {1, 3, 5, 7, 9},  B = {3, 6, 9}, and  C = {2, 4, 6, 8}.   a) A ∪ B:  (b) A ∩ B:  (c) A ∪ C

Q: Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} , A = {1, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8} ,…

A: Definition used-               If  U is a universal set and A is a set inside it the complement of…

Q: {k}, {I, m, o}, {n, p}} of the set U = {k, I, m, n, o, p}. Give the

A: Solution is attached below.

Q: (Assume that in a university with 1000 students. 200 students are taking a course in mathematics,…

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Q: 2. Find sets A, B, C, D such that the sets (An B) U (C\ D), ((An B)U C) \ D, An(BU C) \ D, An(BU (C\…

A: Example of such set A,B,C,D are given below

Q: Let T be the set of all TSU students. Determine if (T, R) a poset or not if R = {(a, b)|a ∈ T, b ∈…

A: 1 We  List all of the ordered pairs in the relation R = {(a, b)|a + b is even} on the set {1, 2, 3,…

Q: Let A = { a, e, i, o, u} and B = { a, b, c, d}. Is A a subset of B ? No.(Why?). Is B a subset of A?…

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Q: Let A=(1, 2,3,4,5,6,7,8,9,10,11,12) how many different non-empty subsets are there in set A

A: Given,            A=(1, 2,3,4,5,6,7,8,9,10,11,12) We have to determine the number of different…

Q: {(x,a),(x,b),(x,c), (y,a),(y,b),(y,c)} is the Cartesian product AXB of two sets given as A = {x,y} B…

A: Let A and B are two sets. Cartesian product of A and B will be denoted by  A×B                A×B…

Q: If (2,0),(0,1),(4,5) and (0,c) are concyclic, and then find c

A: If (2,0),(0,1),(4,5) and (0,c) are concyclic, and then find c

Q: is equivalence and find the equivale [b, b), (c,c) }, A = {a,b,c}

A:

Q: 4. Use set identities or different proof method to show that: (A U B) n (B U A°) = B

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Q: Given Universal Set = { a,b,c,d,e,f,g,h,i,j}; A = { a,b,c,e,g,h}; B = { b,c,e,f,h,i}; C = {…

A:

Q: Show that A = {2,3,4,5} is a proper subset of B = {2,4,5,6,3}

A: A set X will be called a subset of Y, if each elements of X belongs to the set Y . A set X will be…

Q: Let U=​{q,r,s,t,u,v,w,x,y,z}, A=​{q,s,u,w,y}, and B=​{q,s,y,z}. List the elements in the set (A ∩…

A: we know that , X ' = U - X

Q: Consider selecting two elements, a and , from the set A (a,, c d.e). Lt al possible bts of A using…

A: " Since you have posted a two questions, we will solve first question for you. To get another…

Q: Let A=( a, e, i, o, u, ) a) How many proper subsets will A have? b) How many 3-elements subsets will…

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Q: Let X = {a, b, c, d, e} and let T= {X, ø, {a}, {c,d}, {a,c,d}, {b,c,d,e}}, then * (X, T) is not…

A: Option 2 is correct.

Q: Determine whether A=​B, A ⊆ ​B, B ⊆ ​A, A ⊂ ​B, B ⊂ ​A, or if none of these applies.…

A: Subsets are a part of one of the mathematical concepts called Sets.  In set theory, a subset is…

Q: 2. How many 3 element subsets of the set {a, b, c, d, e, f, g, h, i} contain no vowels?

A:

Q: Given R={(a, d), (a, c), (b, d), (c, a), (d, b), (e, d)} on the set {a,b,c,d,e}. Find R-1 А. {(а,…

A: We have given a relation R and we have to find R-1 .

Q: Given that U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}, list…

A: Given, U=1,2,3,4,5,6,7  A=1,2,3,4  B=1,2,5,6 C=3,5,7  We have list all of the members of the set ( A…

Q: Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and    B = {3, 4, 5}. Find A′, B′ , A′ ∩ B′, A ∪ B and hence…

A: Given: Now, The set of all those elements of U which do not belongs to A is called the complement…

Q: Let X = {a, b, c, d,e} and let T = {X, Ø, {a}, {a,d}, {a,e}}, then * O (X,T) is not connected but it…

A: No information is given for topology on Y So i have solved only the middle question

Q: If A (5, 7, 8, 9}, B = {3, 4, 5, 6} and C = {2, 4, 6, 8, 10}; where n is total number of distinct…

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Q: How many proper subsets are there of the set A = {Mallory, Janet, Kaitlynn, Akira}?

A: Given,         The set A= Mallory, Janet, Kaitlynn, Akira .

Q: Number theory

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Q: Let [A1, A2. [B1, B2, C1, C2 be 3 married couples who attended a concert in Windhoek. a) In how many…

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Q: 1.         Consider the sets: A = {a, b, c, d, e, f, h, j}, B = {a, b, i }, C = {f, h} and U =…

A: From the given information, the given sets are:

Q: Let A = {raisin, prune, lemon, pear}, B = {lime, cantaloupe, orange}, and C = {lemon, berry, peach,…

A: Given sets are A=raisin, prune, lemon, pearB=lime, cantaloupe, orangeC=lemon, berry, peach,…

Q: How many subsets are there for the set {h, j}?

A: The given set is {h, j}.It is known that, “If a set contains ‘m’ elements, then the number of…

Q: Prove T = { ... , −56, −42, −28, −14, 0, 14, 28, 42, ... } is a countable set

A:

Q: How many subsets are there of the set A = {Lilliana, Alyvia, Leanne, Imani, Kaleigh}?

A: Given set A = {Lilliana, Alyvia, Leanne, Imani, Kaleigh}

Q: 17) How many elements are in the union of four sets if the sets have 100, 150, 250, and 400…

A: Here, n(A)= 100, n(B), 150, n(C)=250, n(D)=400 n(A∩B)=15, n(A∩C)=15, n(A∩D)=15, n(B∩C)=15,…

Q: If A (5, 7, 8, 9}, B = {3, 4, 5, 6} and C = {2, 4, 6, 8, 10}; wheren is total number of distinct…

A: Consider two sets A and B. Then the union of these two sets contain all the elements in both A and…

Q: Is {1} proper subset of A  A={x,{y},1,2,3,{2,3},{3}}

A: A proper subset of a set A is a subset of A that is not equal to A.Or in other words, if B is a…

Q: Set A contains 6 elements, set B contains 12 elements, and 4 elements are common to sets A and B.…

A: Set A contains 6 elements, set B contains 12 elements, and 4 elements are common to sets A and B.…

Q: Let D be a standard deck of cards, let SV = {A♡, K♡,Q♡, JO}. a) List all the subsets of S♡ that…

A:

Q: 2. If sets A and B are not regular, is ¬A regular? Is A B regular?

A: In this question given that A and B are not regular set We need to find A∪B is regular

Q: Let A={x,y,z,1} and let B= {1,2,4}. If a set  U= (A x B) U (B x A), how many elements are there in…

A: Recall the following facts.

Q: Let A = {8, 9, 10, 11, 12, 14, 15, 16}. How many subsets does A have? How many proper subsets does…

A:

Q: {(x,a), (x,b), (x,c), (y,a), (y,b),(y,c)} is the Cartesian product AXB of two sets given as

A: Given,          x,a,x,b,x,c,y,a,y,b,y,c is the Cartesian product of A×B.

Q: Are the sets Z x Z; ((x.y): x*y?) closed in (R , | |) ? What about the sets (0,1]U(2,3); [0, 00) in

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Q: b) The number of elements of the set A = {{{Ø}}, {{Ø}} n {Ø}, {Ø} U {Ø, {Ø}}} equals

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Q: Let A={blue,orange,red,yellow,green} and B={silver,orange,blue,gold,yellow}. Which sets represents…

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Q: Show that for n attributes A1, A2, A3, ..., A, (Aj A2 Az ... A, ) 2( Aj ) + ( A2 ) + ( A3 ) + ... +…

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Q: Use the Venn diagram below showing the number of elements in regions I through IV to determine the…

A: The venn diagram showing the number of elements in regions I through IV.we have to find number of…

Q: Let X = {a, b, c, d,e} and let T= { X, Ø, {a}, {a,d}, {a,e} }, then * O (X,T) is Hausdorff and…

A:

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.