Let A {1,3,5, ... }, then A is well- ordered.

Q: 2. Let A Ø. If A has exactly n elements, then A has exactly 2" subsets, Vn € N.

A: A is non empty subset of n elements ,then A has exactly 2n subsets,∀n∈ℕ.

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: 8. Let A = {Al, Beth}and B = {up, down, left, right}. Fine %3D

A: # we are entitled to solve one question at a time, please resubmit the other questions if you wish…

Q: 12. Let B be a subset of A. Let |A| = n and |B| = k. What is the number of subsets of A whose…

A: Given B⊂A. A=n and B=k Now if any subset C of A has 3 elements in intersection with B then C≥3 For…

Q: Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8} and E = (0, 2, 4, 6, 8} and P = {2, 3, 5, 7}, then the…

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Q: Let a, = 1 and a₁ + a1 = n² + 2n, n ≥2. Evaluate S

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Q: Let A, = {..., – 2,- 1,0,1,...,i}. Find

A: Ai={..., -2, -1, 0, 1, ......, i} ∩i=1nAi=?

Q: Let X={a,b,c,d), f = ((a,b),(b,a),(c,c),(d,d)}CX×X, and g= ((a,d),(b,a),(c,b),(d,c)}CX×X. Find gof.…

A: Use the definition of composition of functions to solve this problem as in next step.

Q: Let p: A is a proper subset of B. q: A and B are equal. Write: "A is a proper subset of B if and…

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Q: Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that(i) A × (B ∩ C) = (A ×…

A: i) Answer(i) A × (B ∩ C) = (A × B) ∩ (A × C) (proved)

Q: Let A (k,s), t.en the power set of A is:

A: Set of all subsets of A is called power set of A.

Q: How many sets of are in 2-½?

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Q: Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}  List all the…

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Q: Let U={a,b,c,d,e,f,g,h,k}, A={a,b,c,g}, B={d,e,f,g}, C={a,c,f} and D={f,h,k} 1. Compute: a.) A U B…

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Q: Let S = {(1, 0, i), (1, 2, 1)} in C3. Compute S⊥.

A: For the given space in C3 let the desired perpendicular space be (a,b,c). It follows the conditions…

Q: Show that gcd (f1,..., fa) = gcd ( f1, gcd (f2, ... , f,)) for any s > 3.

A: The greatest common divisor of two numbers a and b is the number that divides both a and b. It is…

Q: Let A = { c, d, f, g} B= {f, j} C = {d, g} True or False: B is a proper subset of B? True O False

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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: Show that QQ(2^1/4) is not normal. Further show that Q is subset of Q(2^1/2) and Q(2^1/2) is subset…

A: The objective is to show that Q214 is not normal. Further show that Q is subset of Q212 and Q212 is…

Q: Let A = {1,2,3,4,5,6}, how many different relations are there on a set A?

A: First, we need to know definition  of the Cartesian Product of a set is with itself. The Cartesian…

Q: Let A = {5, 6, 7,9}, B = {x € N|x is odd} , C = {1,2, 3, 4, 5, 6, 7, 8, 9}. Show that A B and ACC.

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Q: List all the subsets of (bear, dog, sheep}. O A. (bear, dog, sheep}, {bear, dog), {bear, sheep},…

A: Given set is {bear,dog,sheep} Now, we need to find all the subsets of given set (i.e) the power set…

Q: Let A = {1, 2, 3, 4, 5}. How many subsets of A have no more than 3 elements?

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Q: 2. Let A = {1,2,3,4,5,6}, how many different relations are there on a set A?

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Q: Let A = { a, e, i, o, u } and B = { a, i, u }. Show that A ∪ B = A

A: A ∪ B ={ a, e, i, o, u } ∪ { a, i, u }           = { a, e, i, o, u }          = A

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and    B = { 2, 3, 5, 7 }. Find A ∩ B and hence show that A…

A: A ∩ B = {1,2,3,4,5,6,7,8,9,10} ∩ {2,3,5,7}           = {2,3,5,7}           = B

Q: 5. If A = I then what is A?

A: Here given as A2=I Taking determinant both side A2=IA2=1A=±1 Thus A is non singular and inverse of A…

Q: Let X = {1,2,3,4} SUCH THAT TX = {4, {2},{1,2},{2,3} , {1, 2, 3},X}: AND Y = {1,3,4} C X, THEN TY =

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Let A = {1,2,3,4,5} B= {6,7,8,9} Emumerate the yuivalenu classeo induces bg the egrivalene melatin…

A: Given that A=1,2,3,4,5B=6,7,8,9 As the relation is not defined, take the equivalence relation…

Q: Let A = {1,2,3} and B = {2,7,9}. Then (ANB)UA = %3D None of the these O ANB O B O A

A: Here two sets are given, we have to find the equivalent expression for the given expression in the…

Q: Let the universal set, U={1,2,3,4,5,6,7}U={1,2,3,4,5,6,7}, A={1,2,4,5,6}A={1,2,4,5,6}, and…

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Q: Let A={a;a=3n and nEN,ns4} ,then A in Roster form is {3,6,9,12}

A: Roster or tabular form: In roster form, all the elements of a set are listed, the elements are being…

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: Let A = {0, 2, 4, 6}, B = {1, 2, 3, 4, 5}, and C = {1, 3, 5, 7}. Find B U (AN C). || {

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Q: if C={}         is {} subset of C ?

A: Question: Is the empty set a subset of itself?

Q: Let A={a; a=3n and nEN, ns4} ,then A in Roster form is {3,6,9,12}

A: To write the given set A in the Roster form, we use the definition of representation of a set in the…

Q: 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

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Q: Let U = {1, 2, 3, 5, 6, 7, 9}, A = {1, 5, 7}, and B = {1, 2, 3}. What is the set (An B)°? O {2, 3,…

A: Sets and relations

Q: (b) Suppose that X,Y and Z are subsets of {1, 2, 3, . . . , 10} and |X| = |Y| = |Z| = 7. Deduce that…

A: Given X, Y and Z are subsets of 1, 2, 3,.......,10. Cardinality X=Y=Z=7. To prove that X ∩ Y ∩ Z is…

Q: Let A = {small, medium, large}, B = {yellow, orange}, and C = {triangle, round}. List the elements…

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Q: Let A, b,, and b, be as defined below. 、目、 [1 2 -1 -2 2 0 2 3 -2 -3 4 0 A= |1 2 2 3 17 2 04 2 3 06…

A: As per bartleby guideline for more than three sub parts asked only first three are to be answered…

Q: Suppose that X is a subset of Y, such that P(Y)>0. Is true or false that P(X|Y) is equal to…

A: It is given that X is a subset of Y This means that PX∩Y=PX...(i) The formula for PX|Y is given by:…

Q: Let Z = {a, b, c, d}. What is the cardinality of the Power Set of Z, |P(Z)|?

A: Power set:Power set of any set S is the set of all subsets of S, including the empty set and S…

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

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Q: Let A = {c, d, f, g), B = {f, j}, and C = (d, g}. CsA A) True (B) False

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Q: a. If A and B are independent, and A and B are independent, show that A and B are also independent.

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Q: Let U = {6, 7, 8, 9, 10, 11, 12}, and A = {6, 7, 8, 9}. List all the members of the given set.  Ā

A: The Universal set U is defined as U = {6, 7, 8, 9, 10, 11, 12}.

Q: 30. (i) Verify that Hall's marriage condition is satisfied for the family {A₁, A₂, A3, A4, A5, A6}…

A: Hall's marriage condition is defined as  let S be the family of finite subsets of X, where the…

Q: Let U = {0,1,2,3,4,5,6,7,8,9,10}; A = {0,1,2,3,5,8}; B={0,2,4,6}; C = {1,3,5,7} %3D Write down a…

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