Q1. Prove the following statement: for all integers a and b, if a is even and b

Question

Q1. Prove the following statement: for all integers a and b, if a is even and b is a multiple of 3, then ab is a multiple of 6.

Q2. If m and n are integers and neither m nor n is zero, is (m + n)/mn a rational number?

Q3. Use proof by contradiction to show that the sum of any rational number and any irrational

number is irrational.

Hint: You can use the following definition to assist you answer Q1 and Q2  

Definition:

A real number r is rational if, and only if, it can be expressed as a quotient of two integers with a nonzero denominator. A real number that is not rational is irrational.

More formally, if r is a real number, then

r is rational integers a and b such that r =    and b 0.

Explanation / Answer

AS per Chegg policy, I am answering only first question:

1.) given a is even number, so a = 2*x where x can be any integer

similarly, b = 3*y where y can be any integer

Now, ab = 2*x * 3*y = 6xy which gives ab is divisible by 6 where xy can be any integer

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