Question

In boolean algebra, proof: (a) x∨y = y if and only if x∧y = x

Answer 1

$1)\;if\;x\wedge y\;=\;x:\\0\wedge0=0\Rightarrow0\vee0=0\;Correct\\0\wedge1=0\Rightarrow0\vee1=1\;Correct\\1\wedge0=0\Rightarrow doesn't\;meet\;requirement\;\\1\wedge1=1\Rightarrow1\vee1=1\;Correct\\2)\;if\;x\vee y=y:\\0\vee0=0\Rightarrow0\wedge0=0\;Correct\\0\vee1=1\Rightarrow0\wedge1=0\;Correct\\1\vee0=1\Rightarrow doesn't\;meet\;requirement\\1\vee1=1\Rightarrow1\wedge1=1\;Correct$

So, checking both cases when one condition true, we get second condition also being true.