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Mathematical Concepts and Problem Solving Assignment

An assignment designed to explore key concepts and problem-solving techniques in discrete mathematics.

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    Mathematical Concepts and Problem Solving Assignment 1. Is the following statement a proposition? Statement: x < y sometimes. A: NO 2. If the universal set is U = { 1, 2, …, 9, 10 } and A = { 1, 4, 7, 10 } and B = { 1, 2, 3, 4, 5 } and C= { 2, 4, 6, 8 } then which of the following represents the set U \ ( A ⊕ B )? A: { 1, 4, 6, 8, 9 } 3. If A, B, and C are any sets, then is the following statement true or false? ( A ∩ B ) ∪ C = A ∩ ( B ∪ C ) A: False 4. If the universal set is U = { 1, 2, …, 9, 10 } and A = { 1, 4, 7, 10 } and B = { 1, 2, 3, 4, 5 } and C= { 2, 4, 6, 8 } then which of the following represents the set B ∩ ( A \ C )? A: { 7, 10 } 5. If A = { x ∈ N | x < 7 }, B = { x ∈ Z | | x – 5 | < 3 }, and C = { 2, 3 } then which of the following list of elements represents the set ( A ⊕ B ) \ C ? A: { 1, 7 } 6. Given the statement, which of the following is the negation? Either x is a negative number or x is not greater than 3. A: Either x is not a negative number and x is greater than 3

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    7. If a 1 = 5 and a k + 1 = 3a k for k > 0 then a 5 = 135 A: True 8. Define a function f from Z to Z by f(n) = (n – 1)*(1 – n). What is the value of f( – 4)? A: - 25 9. Define a function f from Z to Z by f(n) = (n – 1)*(1 – n). What is the value of f(3.5)? A: – undefined 10. If a 1 = 5 and a k + 1 = 3a k for k > 0 then a 4 = 135 A: True 11. Given the following relation on sets A and B defined below, select the correct answer. A = { 1, 2, 3, 4, 5 } B = { a, b, c, d, e } The relation R = { (1, a), (3, b), (5, c), (4, d), (2, e) } A: Is a function that is bijective 12. Define a function f from the product Z × Z to Z by f(a, b) = ab. Is the function 1 to 1? A: False 13. Given the following relation on sets A and B defined below, select the correct answer. A = { a, b, c, d, e } B = { 1, 2, 3, 4, 5 } The relation R = { (a, 2), (b, 1), (c, 3), (d, 5) } A: Is Not a Function

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