Explanation:
To understand why option D is incorrect, let's review the properties of even and odd functions.

An even function is defined as a function that satisfies the property:
f(x) = f(-x) for all x in the domain of the function.

An odd function is defined as a function that satisfies the property:
f(x) = -f(-x) for all x in the domain of the function.

Now, let's analyze each statement:

a) Sum of two even functions is an even function:
Let's consider two even functions, f(x) and g(x).
For any x in the domain of the functions:
f(x) = f(-x) and g(x) = g(-x)

If we take the sum of these two functions, h(x) = f(x) + g(x), then we have:
h(-x) = f(-x) + g(-x) (using the definition of even functions)
= f(x) + g(x) (since f(x) = f(-x) and g(x) = g(-x))

Therefore, h(x) = h(-x), which means the sum of two even functions is an even function.

b) Product of two even functions is an even function:
Let's consider two even functions, f(x) and g(x).
For any x in the domain of the functions:
f(x) = f(-x) and g(x) = g(-x)

If we take the product of these two functions, h(x) = f(x) * g(x), then we have:
h(-x) = f(-x) * g(-x) (using the definition of even functions)
= f(x) * g(x) (since f(x) = f(-x) and g(x) = g(-x))

Therefore, h(x) = h(-x), which means the product of two even functions is an even function.

c) Sum of two odd functions is an odd function:
Let's consider two odd functions, f(x) and g(x).
For any x in the domain of the functions:
f(x) = -f(-x) and g(x) = -g(-x)

If we take the sum of these two functions, h(x) = f(x) + g(x), then we have:
h(-x) = f(-x) + g(-x) (using the definition of odd functions)
= -f(x) - g(x) (since f(x) = -f(-x) and g(x) = -g(-x))

Therefore, h(x) = -h(-x), which means the sum of two odd functions is an odd function.

d) Product of two odd functions is an odd function:
Let's consider two odd functions, f(x) and g(x).
For any x in the domain of the functions:
f(x) = -f(-x) and g(x) = -g(-x)

If we take the product of these two functions, h(x) = f(x) * g(x), then we have:
h(-x) = f(-x) * g(-x) (using the definition of odd functions)
= (-f(x)) * (-g(x)) (since f(x) = -f(-x) and g(x) = -g(-x