Hello RuntyI'll leave all the peripheral bits of the proofs to you. But here are the algebraic proofs that .

a) is the propositional function:

Thenb) is the propositional function:

Thenc) is the propositional function:for

Now

since whenHenced) I'll leave this to you. It's rather similar to (c).

Expand and simplify . Then express the resulting expression in the form , and you'll find that is divisible by .

Can you fill in all the gaps?

Grandad