Proof:A ∩ B ⊆ A

From CS2800 wiki
[math]A \href{/cs2800/wiki/index.php/%E2%88%A9}{∩} B \href{/cs2800/wiki/index.php/%E2%8A%86}{⊆} \href{/cs2800/wiki/index.php?title=A&action=edit&redlink=1}{A} [/math]
Proof:
We want to show that [math]A \href{/cs2800/wiki/index.php/%E2%88%A9}{∩} B ⊆ \href{/cs2800/wiki/index.php?title=A&action=edit&redlink=1}{A} [/math], i.e. that every [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} A \href{/cs2800/wiki/index.php/%E2%88%A9}{∩} B [/math] is also in A. Choose an arbitrary [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} A \href{/cs2800/wiki/index.php/%E2%88%A9}{∩} B [/math]; our new goal is to show that [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} A [/math]. But this comes directly from the definition of [math]\href{/cs2800/wiki/index.php/%E2%88%A9}{∩} [/math], since [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} A \href{/cs2800/wiki/index.php/%E2%88%A9}{∩} B [/math] we know [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} A [/math].