Proving XOR, AND and constant True to be written as NAND I am extending off of a previous question NAND, XOR and AND, and I am attempting to prove that using XOR, AND and constant True can be written to NAND. This is because I was already able to prove NAND with **A∧B** , **A∨B** and **¬A**. Below is the proposition that is equivalent to NAND and I am sadly stuck on where to go now. I was thinking of expanding the last XOR but I feel that I can reduce the left side more before that? > [{A V B} ⊕ {A ⊕ T}] ⊕ A ![Here is the work I have done so far,](

Your expression uses an $\lor$, so that is definitely not good, since you need to use only $\land$, $\oplus$, and $\top$.

Here is something you can do: since $A$ NAND $B \Leftrightarrow \
eg (A \land B)$, and since $P \oplus \top \Leftrightarrow \
eg P$, you have that $A$ NAND $B \Leftrightarrow (A\land B) \oplus \top$.