Question (1) (i) Define Relation .                               (ii) Difference between Union and Intersection of sets with one example

Q: Write true otherwise false if the pairs of sets are equal,{{1}},{1,{1}}

A: Two sets A and B are equal if A and B  have the same elements.

Q: Let f be a function from A to B, and X, Y CB. Show that f¹(XnY) = f'(X) nf ¹(Y).

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Q: (b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs…

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Q: 7. Which of these relations on the set of all people are equivalence relation? a) {(x, y)\x and y…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Select the set that is equivalent to (Cn B) UA. (Cn B)UA (CUB) UA (CnB) nA (CUB) NA

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Q: True or False The intersection of two sets is always a subsetof their union

A: To check the statement

Q: Prove or disprove. Let A, B and C be sets. If AxC=Bx C, then A B

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Q: How to prove properties of sets?

A: Indicator function:Suppose X denotes a set and A is a subset of X. Then, a characteristic function…

Q: C = {whole numbers} and D = %3D {rational numbers} A={multiples of two} and B = {multiples of three}…

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Q: Using properties of sets, show that(i) A ∪ ( A ∩ B ) = A                                (ii) A ∩ ( A…

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Q: (a) Let A, B be sets. Prove that A\(An B) = A\B. You may assume all sets in the question are…

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Q: Give an example of a set that contains nine elements of which two are sets. List three Subsets of…

A: Let the set which contains 9 elements be, A=1,2,3,4,5,6,7,8,9

Q: Identify the missing ordered pairs from the given list. The list of all ordered pairs in the given…

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Q: 1. Show that the function f: N 2. Prove that fof-lomiff f is a function from ran ƒ to dom f. 3. Let…

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Q: True or False a null set is an element of (-2,-1,1,4)

A: The given set is  (-2,-1,1,4)  Null set is not the element of every set. It is the subset of every…

Q: 6. Symmetric Difference Maison The symmetric difference of A and B, denoted by AB, is the set…

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Q: How many symmetric relations on the set A = {1,2, 3, 4, 5, 6, 7, 8} contain the ordered pairs (2,…

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Q: Prove that the functionf: R2 → R defined by f(x, y) = 1 - ² - 4y² is neither injective nor…

A: Injective and surjective function

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

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Q: Prove or disprove. Let A, B and C be sets. If A x C = B x C, then A = B.

A: A cartesian product of two sets A and B is given by the set A×B=a, b | a∈A, b∈B. It is given that…

Q: Discrete Structure (Math) 22(i). Let A = {2,3} be a non-empty set. If R = {(a, b) : a ≤ b and a, b =…

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Q: (a) Prove that ANBCANB.Give an example to show that equality does not always hold.

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Q: R = {(1,1), (1,2), (1,3), (2,3), (7,1), (7,2), (7,3), (4,5), (4,6), (5,6 e (yes or no) whether R has…

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Q: How many relations are there on the set {a, b, c, d}

A: Introduction: The relation is a subset of the Cartesian product of two sets. Since it is a subset of…

Q: Give an example of two sets A and B which are homeomorphic, A is complete and B is not.

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Q: Let A = {1, 2, 3, 4)} and the relation R on A is defined as xRy x<y. а. Find the relation R in…

A: We are given, A = {1, 2, 3, 4} and the relation R on A is defined as xRy &lt;=&gt; x&lt;y.

Q: How many relations are there on the set that contain the pair (a, a)?

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