a) Draw the Venn diagram or provide area numbers for the following combination of the sets A, B, and C. (AU C) – (BOC) OR The shaded areas are:. b) Then decide truth values of following statements: a) vx(xE A AxE B ^ x € C→x € (A U C) - (BOC)) TRUE FALSE b) vx(xE AAxE BAXE C-x € (A U C) – (BOC)) c) vx(xE AAx E BAXE C-x € (A U C) – (BOC)) TRUE FALSE TRUE FALSE

Q: 12] and a3 = -20 4 -------- Let a₁ = h 5 2 The set {a1, a2, a3} will span R³ unless h = 0

A:

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A: our objective is to find the solution.

Q: - For all sets A, B and C. Is (An B) U C =An (Bu C)? Justify your statement. You may ju

A: Yes, the above statement is false and the proof of above statement is given below:

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Q: 10. Let A, B, and C be sets. Use the identities to show that (A U B) n (B U C) n (A U C) = Ā n Bn T.

A:

Q: 1. example of sets A and B for which A B but Ag B.

A: Cardinality of a set is number of elements in the set.

Q: (d) An (BNC) = (Ar (e) If A C B, then (AUC) C (BUC) (f) ACB if and only if (AUB) = B

A:

Q: 3. Let A and B be two sets. Use set operation properties to prove the identity ,AÐB = AUBU (AO B).

A: To prove the identity

Q: 2. If A = {a,b,c}, B = {1,2,3}, C = {x}, and D = 0, list all of th the following sets. (a) Ax B (c)…

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Q: 1. Use set identities or different proof method to show that: a) (B–A)U(C – A) = (BUC)-A b) (A-C)n(C…

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Q: 1. Determine which of the following statements are true for all sets A, B, C, and D. If a double…

A: .

Q: 6. Let A, B, and C be sets. Verify the following (you can use a membership table) a) An (BUC) =…

A: ∩ : and  ∪ : or  We have to prove :

Q: 1. Let A, B, and C be sets. Given A C B, show that (a) AnC C BnC. (b) ВС А.

A:

Q: 5. Consider the following statement: For all sets A, B, and C, then AU (BNC) = (AUB) nC. Either…

A: Let value of set A,set B and set C are respectively. A={1,2,3,6,7} B={3,7,8,9} C={2,3,6,9}

Q: What can you say about the sets A and B if AB=A?

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A: The answer for the above question is given below please do upvote if you like the solution thank you

Q: 10. Place the correct symbol from the list C, =, 2 between each pair of sets below a) AUB, AU (B −…

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Q: Given: LM || PQ. M MZQLP - M2NMI. Prove: AQLP - ANML. Statements Reasons LM || PO Given 2. ZIPQ =…

A: ∆QLP~∆NML (AA similarity) Reason is AA similarity .

Q: (c) Every element in the set {0, 1, 2} is greater than or equal to half of its square. i. Original…

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Q: 2. If A = {a,b,c}, B = {1,2,3}, C = {x}, and D = 0, list all of the elements in each of the…

A: We have to find Cartesian product of part (c) and part (d)