Various Problems in Discrete Mathematics Prove Each Directly 1 The product of any two even integers

Various Problems in Discrete Mathematics

Prove Each Directly

1 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

2 [-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

3 Every month has exactly 30 days

Let a, b, and c be any real numbers Then a
only if there

is a positive real number x such that a + x – b Use this
fact to prove

each

4 If a+c is less than b+c, then a is less than b

Determine if the given sets are equal

5 {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)’