I am having a bit of a brain malfunction. I am working through a functional programming class and I am trying to in parallel fake some knowledge of discrete mathematics.
I am working through a simple example of expanding $$(a^0 \lor a^1) \land (b^0 \lor b^1)$$
to
$$(a^0 \land b^0) \lor (a^0 \land b^1) \lor (a^1 \land b^0) \lor (a^1 \land b^1)$$
I think I understand that I should start with the distributive property to expand but I am not sure how to do this with 4 distinct terms.
Sorry, this is probably a very silly question - I really should set aside time to take a proper discrete mathematics course but in the meantime, can someone explain this to me? I would be very grateful.
Thanks in advance!
Begin by treating $a^0\lor a^1$ as a single quantity and distributing it, and then distribute $b^0$ and $b^1$ in their separate conjuncts:
$$\begin{align*} (a^0\lor a^1)\land(b^0\lor b^1)&=\big((a^0\lor a^1)\land b^0\big)\lor\big((a^0\lor a^1)\land b^1\big)\\ &=(a^0\land b^0)\lor(a^1\land b^0)\lor(a^0\land b_1)\lor(a^1\land b^1) \end{align*}$$