11 Set Theory: Cardinality of Infinite Sets Task: Refer to Question 11 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing 12 Partial Differential Equations: Heat Equation Task: Refer to Question 12 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing

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A: Step 1: Question 1 Note that the prime factorization of 32 is 32=25, i.e., any group of order 32 is…

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A: Note: General solution= Complementary function (C.F.) + Particular integral (P.I.)

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A: 14. Option a is correct. y=−6x515. Option a is correct. f(25​).

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A: 9. b. even10. c. reflected in the x-axis and translated upwards

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A: Question 25:Question 26:Question 27:

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Q: Let W be the subspace spanned by the given vectors. Find a basis for W. 1 0 -1 1 W1 = W2 = 8 -7 ↓1

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A: (a)(b)

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A: Prompt: Analyze the logical expression:∼A ∨ ∼G Given:A = TrueG = TrueStep-by-Step Analysis:Evaluate…

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