Find incomparable elements in the poset (P({1, 2, 3]), s) Note: P: power set {1, 2} and {1, 2, 3} (1) and (2) (2, 3) and (3) (1) and (1,2) (3) and {1, 2}

Q: Write down all elements of {I, J, K} x {W, X}. (Enter your answer in set notation.)…

A: The given problem is to find the Cartesian product of the given sets {I,J,K} and {W,X}.

Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: The table below shows the values of predicates P(x, y) for every possible combination of values of…

A: Given truth table for P(x,y) isHere we have to determine the truth value of given expressions.

Q: Answer the following questions for the poset ({{1}, {2}, {4}, {1, 2}, {1, 4), (2, 4), (3, 4), (1, 3,…

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Q: Given the function f= {(n,n²)such thatn< 3,n€N} as a set of ordered pairs in set-builder notation,…

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Q: Explain each step of this proof that C(5, 5) + C(6, 5) + C(7, 5) = C(8, 6): Proof. C(5, 5) + C(6, 5)…

A: The proof of the statement is given in the explanation part.Explanation:Steps and explanations are…

Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are %3D %3D two sets. find R = {(x, y): x E X and y E Y…

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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 S1= {1, 5, 10, 15, 20} and let S2 = {1, 2, 3, 4, 5}. What is: (a) S1 ∪ S2 (b) S1 ∩ S2 (c) S1 –…

A: Given: The given sets are S1=1, 5, 10, 15, 20 and S2=1, 2, 3, 4, 5. To find: The main aim is to find…

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Using the Gentzen System G prove ⊢ (A → B) → ((¬A → B) → B) Clearly indicate which rule was applied…

A: We should use the decomposition tree to prove the given logical statement. The given statement is…

Q: Uist all subsets of the set C-(1, 2, 3).

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Q: (e) Given the sets A = {-5, –3,0, 1, 5} and B = {-4, –3,0, 1, 5, 6}. Find AN B. (A) {-5, –4, –3, 0,…

A: We have to find out the intersection part

Q: work): Evaluate the det(A) using any method (but make sure to show your A -2 3 -12 12 -14 19 -20 31…

A: Given:The matrix is given by .To Find:We have to find the determinant of the matrix .

Q: Let u = (2, -2, 3), v = (1, -3, 4), and w=(3, 6, -4). Evaluate the following 1. ||3u-5v+w||…

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Q: Consider the set A = {2, 4, 6, 8} with an operation defined by the table. 2 4 6 8 2 8…

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Q: {3,5,6,7,9} (a) State A in standard roster form. A =. (b) Let B := A n{1,2,3,4,5, 6, 7,8}. State B…

A: Given A={3,5,6,7,9} B=A∩{1,2,3,4,5,6,7,8} (b) To state Bin the roster form. (c) To calculate…

Q: {0,1,2,5,6,7} (a) State A in standard roster form. A = (b) Let B := A n{1,2,3, 4, 5, 6, 7,8}. State…

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Q: 4. Let A = {a,b), B = {1,2], and C= {1,2,3), and see Definitions 2.2.4 and 2.2.7. (a) List the…

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Q: (10) Prove that P(A)n P(B) is equal to P(An B) for any sets A and B. What can we say if the…

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Q: (5) Let S be the set {1, 2, {3,4}, 6, Z}. Decide if these statements are true or false. (a) 6 ES (b)…

A: This question is related to set.

Q: In the following list, select all the correct statements, if (4,) is a poset and for any elements…

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Q: (Q × {-T, 1})U{-3n, –27}UZ is O an empty set O an uncountable set O a countable set

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Q: Let A = {1, 2, 3, 4, 5} and R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2,…

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