A Boolean function is said to be ‘even’ if it has an even number of 1s (and thus also an even number

A Boolean function is said to be ‘even’ if it has an even
number of 1s (and thus also an even number of 0s) in its truth . Otherwise, it
is said to be ‘odd’. In other words, an even function has an even number of
terms in its minterm expansion, while an odd function has an odd number of
terms in its minterm expansion. Demonstrate the following properties: If both f
and g are even, then f ˚ g is even. If both f and g are odd, then f ˚
g is even. If f is even and g is odd, then f ˚ g is odd.