State the formula for the Principle of Inclusion and Exclusion for 3 sets. Draw a Venn diagram showing X'nY if X SYSZ

Q: 2.5.22. Let A, B,C be three sets. Prove that if A \ B C C, then A \C C B.

A: Given: Let A,B,C be the three sets. A-B contained in C

Q: 13. Find the Cartesian product A x B of the sets A = {12, 9, 10} and B = {14,4}

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Q: How many subsets does the set X = {r, s, t, 10, 20, 15} have? %3D

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Q: If #: $ a,b,c} which of these celations are a funchion? Emplain, cab) CS

A: Solution : Given :    A= {a, b, c}  Set of relations are      a)    { (a, b), (b, c), (c, c) }…

Q: List all the subsets of the set A = {a, b, c, d}

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Q: . How many relations are there on the set S = {2, 4, 6}? 892 512 none of these 1024

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Q: b. How many elements are in the set {a, {a, b}, {a} }? C. For each positive integer x, let A1` =…

A: Use the definition of set and its elements to solve this problem as in next step.

Q: Select all of the following sets that could be the set A if AC {5, 7, 11, 13, 17, 19}. O{5, 7, 11,…

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Q: 8. Show that the set (0, 1) – {1/2, 1/3, 1/4, -..} is uncountable.

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Q: Q26. Which subset immediately precedes the subset {X7, X5, X3, X2, X1} of the set S= {X7, X6, X5,…

A: Total number of subset of S =2^8 = 256 Now let's find subsets having 5 elements. {x7,x6,x5,x4,x3}…

Q: Suppose we have a set A={1, 2, 3, 4, 5, 6}. What is the partition of A into three parts? Make sure…

A: We can partition of set A as below

Q: The symmetric difference of sets A and B, consists of those elements which belong to A or B but not…

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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: How many relations are there on the set S = {2, 4, 6}?

A: We know that, the number of relations of a set containing n element is 2n^2. Given that S = {2,4,6}

Q: List down the elements of the following sets {x ∈ ℝ : x2 + 5x = -6}

A: Explanation of the answer is as follows

Q: Suppose that A is a set and {Bn}nɛ1 is an indexed family of sets. Prove that A - U B, = N(A – B„,).…

A: Suppose that A is a set and Bnn∈I is an indexed family of sets. Then we have to prove that…

Q: 1. Give at least 5 pairs of numbers a and b. For each of those pairs find at least 10 elements of…

A: We need to find at least 5 pairs of numbers a and b. For each of those pairs  at least 10 elements…

Q: 6. List the subsets of {a, B,r, A}.

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Q: d. A с S B

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Q: Let A = {1, 2}. List all the subsets of A. Let B = {1, 2, 3}. List all the subse

A: 1. Let A=1,2find the subsets of A.2.Let B=1,2,3list the subsets of B which are not contained in A.

Q: Find the number of relations from the set A {a, b, c} to the set B = {1,3}

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Q: Determine whether each of these pairs of set are equal 1 (5,6,7,8,9,10) (1,2,3,3,4,4) = 2.…

A: We know that two sets A and B can be equal only if each element of set A is also the element of the…

Q: 2. 1) Lot A = P(Ø), B = P([a,b}), and C = P({a,c}) where P(S) is the power %3D %3D set of S. Find…

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Q: 3. Find a subset of P({1,2,3}) with four elements.

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Q: VII.1. Describe the set (R × Z) ∩ (Z × R)

A: We have to describe the set (R × Z) ∩ (Z × R).

Q: Let D=​{10​,13​,15​}, E=​{10​,12​,13​,14​} and F=​{9​,11​,12​,13​,15​}.   List the elements in the…

A: Given,  Sets D=​10​,13​,15​ E=​10​,12​,13​,14​  and  F=​9​,11​,12​,13​,15​ We have to list the…

Q: Consider U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} as the universal set and let C = {1,4,9}, D =…

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Q: 15. consider the following sets: U={-5,-4,-3,-2,-1,0,1,2,3,4,5}; A={x: x^2=25}…

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Q: 13. consider the following sets: U={-5,-4,-3,-2,-1,0,1,2,3,4,5}; A={x: x^2=25} ;B={-5,0,1,2,3,4,5};…

A: Given that U=-5,-4,-3,-2,-1,0,1,2,3,4,5 A=x:x2=25 B=-5,0,1,2,3,4,5 C=x:x2-5x+6=0 We have to find A∩B