Discrete Math Proof give explanation Show that 1 the product

Discrete Math Proof (give explanation):

Show that
(1) the product of two odd numbers is odd,
(2) and that the product of two numbers, at least one of which is even, is
even.

Solution

(1) the product of two odd numbers is odd,

let n be a even number

(n+1) , (n+3) , (n+5) are odd

product of two odd numbers

(n+1)(n+3) = n^2+4n+3

here n is even square root of even is even

4*n is even

sum of even and odd is odd

hence it is odd

product of two numbers, at least one of which is even, is
even.

n (n+1)

n^2+n

n^2 even and n even hence even