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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 Assignment1.Is the following statement a proposition?Statement: x < y sometimes.A: NO2. If the universal set is U = { 1, 2, …, 9, 10 } andA= { 1, 4, 7, 10 } andB= { 1, 2,3, 4, 5 } and C= { 2, 4, 6, 8 } then which of the following represents the setU\(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: False4. If the universal set is U = { 1, 2, …, 9, 10 } andA= { 1, 4, 7, 10 } andB= { 1, 2,3, 4, 5 } andC= { 2, 4, 6, 8 } then which of the following represents the setB∩(A\C)?A: { 7, 10 }5.IfA= {x∈N|x< 7 },B= {x∈Z| |x–5 | < 3 }, and C = { 2, 3 } then whichof 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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