Assignment:
Q1. The product of any two even integers is even.
Prove by cases, where n is an arbitrary integer and Ixl denotes the absolute value of x.
Q2. [-x]=[x] (*Brackets are the x's is the absolute value symbol)
Give a counterexample to disprove each statement, where P(x) denotes an arbitrary predicate.
Q3. Every month has exactly 30 days.
Let a, b, and c be any real numbers. Then a < b if and only if there is a positive real number x such that a + x - b. Use this fact to prove each.
Q4. If a+c is less than b+c, then a is less than b
Determine if the given sets are equal.
Q5. {x, {y}}, {{x},y}
Let A = {a, e, f, g,i}, B = {b, d, e, g, h}, C = {d, e, f, h, i}, and U= {a,b,... ,k}. Find each set.
6. (A U B)'
Provide complete and step by step solution for the question and show calculations and use formulas.