Let a be an even function and B be an odd function, then the sum difference product quotient of a and B, the sum difference product quotient of a and a, and the sum difference product quotient of B and B are odd or even functions respectively? Even + - odd =? (even or odd) even × / odd =? (even or odd) Even + - even =? (even or odd) even × / even =? (even or odd) Odd + - odd =? (even or odd) odd × / odd =? (even or odd)

Let a be an even function and B be an odd function, then the sum difference product quotient of a and B, the sum difference product quotient of a and a, and the sum difference product quotient of B and B are odd or even functions respectively? Even + - odd =? (even or odd) even × / odd =? (even or odd) Even + - even =? (even or odd) even × / even =? (even or odd) Odd + - odd =? (even or odd) odd × / odd =? (even or odd)

Let a be f (x), B be g (x)
Because a is even and B is odd
So f (x) = f (- x), G (- x) = - G (x)
F (- x) + G (- x) = f (x) - G (x), so the sum of a and B is neither odd nor even
F (- x) - G (- x) = f (x) + G (x), so the difference between a and B is even function
F (- x) × g (- x) = - f (x) × g (x), so the product of a and B is an odd function
F (- x) / g (- x) = - f (x) / g (x), so the quotient of a and B is an odd function
F (- x) + F (- x) = f (x) + F (x), so the sum of a and a is even
F (- x) - f (- x) = f (x) - f (x), so the difference between a and a is even function
F (- x) × f (- x) = f (x) × f (x), so the product of a and a is even function
F (- x) / F (- x) = f (x) / F (x), so the quotient of a and a is even
F (- x) × f (- x) = f (x) × f (x), so the product of a and a is even function
G (- x) + G (- x) = - G (x) - G (x), so the sum of B and B is an odd function
G (- x) - G (- x) = - [g (x) - G (x)], so the difference between B and B is an odd function
G (- x) × g (- x) = [g (x) × g (x)], so the product of B and B is even function
G (- x) / g (- x) = [g (x) / g (x)], so the sum of B and B is even